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We study a holographic model in which the striped structure of charge density is spontaneously formed over an ionic lattice which breaks the translational symmetry explicitly. The effect of commensurate lock-in between the spontaneous stripes and the ionic lattice is observed when the lattice amplitude is large enough. We investigate the optical conductivity as a function of frequency in commensurate state and compare its characteristics during the phase transition from metallic phase to insulating phase. Notably, we find that the DC resistivity in lock-in state increases algebraically with lowering temperature, which is in line with the phenomenon observed in the holographic model for simulating the experimental behavior of Mott insulator in [1]. In addition, at lower temperature the pinning effect is observed for both unlock-in and lock-in states. This holographic model successfully demonstrates the commensurate lock-in signatures, and provides more information for understanding the interplay between ionic lattices and electronic lattices by holography. [ABSTRACT FROM AUTHOR]

We conduct an exhaustive study of the interior geometry of a family of asymptotically AdSd+1 hairy black holes in an analytically controllable setup. The black holes are exact solutions to an Einstein-Maxwell-Dilaton theory and include the well-known Gubser-Rocha model. After reviewing the setup, we scrutinize the geometry beyond the horizon, finding that these backgrounds can exhibit timelike or Kasner singularities. We generalize the no inner-horizon theorem for hairy black holes to accommodate these findings. We then consider observables sensitive to the geometry behind the horizon, such as Complexity = Anything and the thermal a-function. In the Kasner case, we propose a new variant of complexity that characterizes the late-time rate by the Kasner exponents, extending previous work by Jørstad, Myers and Ruan. Additionally, we elucidate the power-law behavior of the thermal a-function near the singularity, directly relating it to the Kasner exponents. Finally, we introduce axion-like fields in the Gubser-Rocha model to study the impact of translational symmetry breaking on the black hole interior. We show that Kasner singularities occur for both explicit and spontaneous symmetry breaking, with the Kasner exponents depending on the strength of broken translations only in the latter case. [ABSTRACT FROM AUTHOR]

The holographic superconductor is the holographic dual of superconductors. We recently identified the dual Ginzburg-Landau (GL) theory for a class of bulk 5-dimensional holographic superconductors (arXiv:2207.07182 [hep-th]). However, the result is the strong coupling limit or the large-Nc limit. A natural question is how the dual GL theory changes at finite coupling. We identify the dual GL theory for a minimal holographic superconductor at finite coupling (Gauss-Bonnet holographic superconductor), where numerical coefficients are obtained exactly. The GL parameter κ increases at finite coupling, namely the system approaches a more Type-II superconductor like material. We also point out two potential problems in previous works: (1) the “naive” AdS/CFT dictionary, and (2) the condensate determined only from the GL potential terms. As a result, the condensate increases at finite coupling unlike common folklore. [ABSTRACT FROM AUTHOR]

We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point functions, the analysis is performed in the limit where the two-point function becomes simple and we compare the results with those of other previous studies. We confirm the exponential growth of Krylov complexity in the very low temperature regime. In general, Krylov complexity grows at most linearly at very late times in any system with a bounded energy spectrum. Therefore, we have to focus on the initial growth to see differences in the behaviors of systems or operators. Since the DSSYK model is such a bounded system, its chaotic nature can be expected to appear as the initial exponential growth of the Krylov complexity. In particular, the time at which the initial exponential growth of Krylov complexity terminates is independent of the number of degrees of freedom. More generally, and not limited to the DSSYK model, we systematically and specifically study the Lanczos coefficients and Krylov complexity using a toy power spectrum and deepen our understanding of those initial behaviors. In particular, we confirm that the overall sech-like behavior of the power spectrum shows the initial linear growth of the Lanczos coefficient, even when the energy spectrum is bounded. [ABSTRACT FROM AUTHOR]

This paper shows that the bulk metric of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of two probe scalar operators by solving Gel’fand-Levitan-Marchenko integral equation. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes a new method to “measure” the corresponding holographic spacetime for a material that has holographic dual but also provides an approach to experimentally check if a system has holographic dual. [ABSTRACT FROM AUTHOR]

In large N chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the “scramblon.” We study self-interactions of the scramblon in variants of the Sachdev-Ye-Kitaev model. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to out-of-time-order correlators becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature. [ABSTRACT FROM AUTHOR]

The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without introducing any order parameter. We then classify the Mott gap, depending on the shape of the gap in the density of states and whether the Fermi surface is touching the valence bond or not, into three classes: i) Symmetric gap, ii) Asymmetric gap with isolated Fermi sea. iii) Asymmetric gap with Fermi sea touching the valence band. Finally, we identify possible non-minimal gauge interactions that produce a flatband without symmetry breaking. [ABSTRACT FROM AUTHOR]

We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena. [ABSTRACT FROM AUTHOR]

Abstract We generalize the potential reconstruction method to set up a dynamical Einstein-Born-Infeld-dilaton model, which we then use to study holographic quarkonium melting in an external magnetic field. The non-linear nature of the model allows to couple the magnetic field to the quarkonium inner structure without having to introduce back-reacting charged flavour degrees of freedom. The magnetic field dependent melting temperature is computed from the spectral functions and suggests a switch from inverse magnetic to magnetic catalysis when the magnetic field increases. We also discuss the differences due to the anisotropy brought in by the external field.

Abstract We conduct an exhaustive study of the interior geometry of a family of asymptotically AdS d+1 hairy black holes in an analytically controllable setup. The black holes are exact solutions to an Einstein-Maxwell-Dilaton theory and include the well-known Gubser-Rocha model. After reviewing the setup, we scrutinize the geometry beyond the horizon, finding that these backgrounds can exhibit timelike or Kasner singularities. We generalize the no inner-horizon theorem for hairy black holes to accommodate these findings. We then consider observables sensitive to the geometry behind the horizon, such as Complexity = Anything and the thermal a-function. In the Kasner case, we propose a new variant of complexity that characterizes the late-time rate by the Kasner exponents, extending previous work by Jørstad, Myers and Ruan. Additionally, we elucidate the power-law behavior of the thermal a-function near the singularity, directly relating it to the Kasner exponents. Finally, we introduce axion-like fields in the Gubser-Rocha model to study the impact of translational symmetry breaking on the black hole interior. We show that Kasner singularities occur for both explicit and spontaneous symmetry breaking, with the Kasner exponents depending on the strength of broken translations only in the latter case.

Abstract We study a holographic model in which the striped structure of charge density is spontaneously formed over an ionic lattice which breaks the translational symmetry explicitly. The effect of commensurate lock-in between the spontaneous stripes and the ionic lattice is observed when the lattice amplitude is large enough. We investigate the optical conductivity as a function of frequency in commensurate state and compare its characteristics during the phase transition from metallic phase to insulating phase. Notably, we find that the DC resistivity in lock-in state increases algebraically with lowering temperature, which is in line with the phenomenon observed in the holographic model for simulating the experimental behavior of Mott insulator in [1]. In addition, at lower temperature the pinning effect is observed for both unlock-in and lock-in states. This holographic model successfully demonstrates the commensurate lock-in signatures, and provides more information for understanding the interplay between ionic lattices and electronic lattices by holography.

Abstract The holographic superconductor is the holographic dual of superconductors. We recently identified the dual Ginzburg-Landau (GL) theory for a class of bulk 5-dimensional holographic superconductors (arXiv:2207.07182 [hep-th]). However, the result is the strong coupling limit or the large-N c limit. A natural question is how the dual GL theory changes at finite coupling. We identify the dual GL theory for a minimal holographic superconductor at finite coupling (Gauss-Bonnet holographic superconductor), where numerical coefficients are obtained exactly. The GL parameter κ increases at finite coupling, namely the system approaches a more Type-II superconductor like material. We also point out two potential problems in previous works: (1) the “naive” AdS/CFT dictionary, and (2) the condensate determined only from the GL potential terms. As a result, the condensate increases at finite coupling unlike common folklore.

Abstract We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point functions, the analysis is performed in the limit where the two-point function becomes simple and we compare the results with those of other previous studies. We confirm the exponential growth of Krylov complexity in the very low temperature regime. In general, Krylov complexity grows at most linearly at very late times in any system with a bounded energy spectrum. Therefore, we have to focus on the initial growth to see differences in the behaviors of systems or operators. Since the DSSYK model is such a bounded system, its chaotic nature can be expected to appear as the initial exponential growth of the Krylov complexity. In particular, the time at which the initial exponential growth of Krylov complexity terminates is independent of the number of degrees of freedom. More generally, and not limited to the DSSYK model, we systematically and specifically study the Lanczos coefficients and Krylov complexity using a toy power spectrum and deepen our understanding of those initial behaviors. In particular, we confirm that the overall sech-like behavior of the power spectrum shows the initial linear growth of the Lanczos coefficient, even when the energy spectrum is bounded.

Abstract This paper shows that the bulk metric of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of two probe scalar operators by solving Gel’fand-Levitan-Marchenko integral equation. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes a new method to “measure” the corresponding holographic spacetime for a material that has holographic dual but also provides an approach to experimentally check if a system has holographic dual.

Abstract In large N chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the “scramblon.” We study self-interactions of the scramblon in variants of the Sachdev-Ye-Kitaev model. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to out-of-time-order correlators becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature.

Abstract The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without introducing any order parameter. We then classify the Mott gap, depending on the shape of the gap in the density of states and whether the Fermi surface is touching the valence bond or not, into three classes: i) Symmetric gap, ii) Asymmetric gap with isolated Fermi sea. iii) Asymmetric gap with Fermi sea touching the valence band. Finally, we identify possible non-minimal gauge interactions that produce a flatband without symmetry breaking.

Abstract We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena.

Abstract Holographic quantum matter exploits the AdS/CFT correspondence to study systems in condensed matter physics. An example of these systems are strongly correlated semimetals, which feature a rich phase diagram structure. In this work, we present a holographic model for a Dirac semimetal in 2 + 1 dimensions that features a topological phase transition. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. The phase diagram for different values of the relevant coupling constants is obtained. The different phases are characterized by distinct dispersion relations for probe fermionic modes in the AdS geometry. We find semi-metallic phases characterized by the presence of Dirac cones and an insulating phase featuring a mass gap with a mild anisotropy. Remarkably, we find as well an anisotropic semi-Dirac phase characterized by a massless a fermionic excitation dispersing linearly in one direction while quadratically in the other.

Abstract We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.

Abstract We consider a model of a holographic 2+1d CFT interacting with an oscillating background gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary field theory. However, we also show that if timelike singularities of Kasner type are permitted then a time independent solution that may be interpreted as a Floquet state of the system can be constructed. In this state the system exhibits either Hall conductivity or kinetic induction, and we numerically evaluate the Kasner exponents for a range of boundary conditions. This model may contribute to the ongoing discussion on the validity and meaning of the Kasner metric in the AdS/CFT correspondence and its application in cosmology.

Abstract We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined at t = 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, after t = 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics.

Abstract We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We corroborate the observation that the presence of a peak in spread complexity before its saturation, is a characteristic feature in chaotic systems. We find that, in general, the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. However, there appears to be a maximal universal bound determined by the symmetries and dimension of the Hamiltonian, which is realized by the thermofield double state (TFD) at infinite temperature. We also find that the time scales at which the spread complexity and spectral form factor change their behaviour agree with each other and are independent of the chaotic properties of the systems. In the case of spectral complexity, we identify that the key factor determining its saturation value and timescale in chaotic systems is given by minimum energy difference in the theory’s spectrum. This explains observations made in the literature regarding its earlier saturation in chaotic systems compared to their integrable counterparts. We conclude by discussing the properties of the TFD which, we conjecture, make it suitable for probing signatures of chaos in quantum many-body systems.

Abstract We investigate the link between quantum position-verification (QPV) and holography established in [1] using holographic quantum error correcting codes as toy models. By inserting the “temporal” scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.

Abstract We study the entanglement entropy associated with a holographic RG flow from AdS7 to AdS4 × ℍ 3, where ℍ 3 is a 3-dimensional hyperbolic manifold with curvature κ. The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c-function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ. We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy.

Abstract The dynamics of first-order phase transitions in strongly coupled systems are relevant in a variety of systems, from heavy ion collisions to the early universe. Holographic theories can be used to model these systems, with fluctuations usually suppressed. In this case the system can come close to a spinodal point where theory and experiments indicate that the behaviour should be similar to a critical point of a second-order phase transition. We study this question using a simple holographic model and confirm that there is critical slowing down and scaling behaviour close to the spinodal point, with precise quantitative estimates. In addition, we determine the start of the scaling regime for the breakdown of quasistatic evolution when the temperature of a thermal bath is slowly decreased across the transition. We also extend the analysis to the dynamics of second-order phase transitions and strong crossovers.

Abstract We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with q-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite q and analytically at large q. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large q limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large q, leading to classical dynamics of the operator size growth with dissipation.

Abstract This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the D3/D7 brane configuration. The research explores the non-linear response of the longitudinal current J when subjected to an external electric field E at both zero and finite temperatures. At zero temperature, the study identifies a potential quantum phase transition in the J-E relationship, driven by background parameters the particle mass, and axial gauge potential. This transition is characterized by a unique reconnection phenomenon resulting from the interplay between WSM-like and conventional nonlinear conducting behaviors, indicating a quantum phase transition. Additionally, at non-zero temperatures with dissipation, the system demonstrates first- and second-order phase transitions as the electric field and axial gauge potential are varied. The longitudinal conductivity is used as an order parameter to identify the current-driven phase transition. Numerical analysis reveals critical exponents in this non-equilibrium phase transition that show similarities to mean-field values observed in metallic systems.

Abstract Pole-skipping refers to the special phenomenon that the pole and the zero of a retarded two-point Green’s function coincide at certain points in momentum space. We study the pole-skipping phenomenon in holographic Green’s functions of boundary operators that are dual to massive p-form fields and the dRGT massive gravitational fields in the AdS black hole background. Pole-skipping points for these systems are computed using the near horizon method. The relation between the pole-skipping points of massive fields and their massless counterparts is revealed. In particular, as the field mass m is varied from zero to non-zero, the pole-skipping phenomenon undergoes an abrupt change with doubled pole-skipping points found in the massive case. This arises from the breaking of gauge invariance due to the mass term and the consequent appearance of more degrees of freedom. We recover the gauge invariance using the Stueckelberg formalism by introducing auxiliary dynamical fields. The extra pole-skipping points are identified to be associated with the Stueckelberg fields. We also observe that, as the mass varies, some pole-skipping points of the wave number q may move from a non-physical region with complex q to a physical region with real q.

Abstract The rapid development of quantum science and technology is leading us into an era where quantum many-body systems can be comprehended through quantum simulations. Holographic duality, which states gravity and spacetime can emerge from strongly interacting systems, then offers a natural avenue for the experimental study of gravity physics without delving into experimentally infeasible high energies. A prominent example is the simulation of traversable wormholes through the wormhole teleportation protocol, attracting both theoretical and experimental attention. In this work, we develop the theoretical framework for computing the fidelity of wormhole teleportation in N-qubit systems with all-to-all interactions, quantified by mutual information and entanglement negativity. The main technique is the scramblon effective theory, which captures universal out-of-time-order correlations in generic chaotic systems. We clarify that strong couplings between the two systems are essential for simulating the probe limit of semi-classical traversable wormholes using strongly interacting systems with near-maximal chaos. However, the teleportation signal diminishes rapidly when reducing the system size N, requiring a large number of qubits to observe a sharp signature of emergent geometry by simulating the Sachdev-Ye-Kitaev model. This includes both the causal time-order of signals and the asymmetry of the teleportation signal for coupling with different signs. As a comparison, the teleportation signal increases when reducing N in weakly interacting systems. We also analyze the fidelity of the generalized encoding scheme in fermionic string operators.

Abstract We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases as due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The Rényi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time.

We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question. [ABSTRACT FROM AUTHOR]

We consider a model of a holographic 2+1d CFT interacting with an oscillating background gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary field theory. However, we also show that if timelike singularities of Kasner type are permitted then a time independent solution that may be interpreted as a Floquet state of the system can be constructed. In this state the system exhibits either Hall conductivity or kinetic induction, and we numerically evaluate the Kasner exponents for a range of boundary conditions. This model may contribute to the ongoing discussion on the validity and meaning of the Kasner metric in the AdS/CFT correspondence and its application in cosmology. [ABSTRACT FROM AUTHOR]

Holographic quantum matter exploits the AdS/CFT correspondence to study systems in condensed matter physics. An example of these systems are strongly correlated semimetals, which feature a rich phase diagram structure. In this work, we present a holographic model for a Dirac semimetal in 2 + 1 dimensions that features a topological phase transition. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. The phase diagram for different values of the relevant coupling constants is obtained. The different phases are characterized by distinct dispersion relations for probe fermionic modes in the AdS geometry. We find semi-metallic phases characterized by the presence of Dirac cones and an insulating phase featuring a mass gap with a mild anisotropy. Remarkably, we find as well an anisotropic semi-Dirac phase characterized by a massless a fermionic excitation dispersing linearly in one direction while quadratically in the other. [ABSTRACT FROM AUTHOR]

We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We corroborate the observation that the presence of a peak in spread complexity before its saturation, is a characteristic feature in chaotic systems. We find that, in general, the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. However, there appears to be a maximal universal bound determined by the symmetries and dimension of the Hamiltonian, which is realized by the thermofield double state (TFD) at infinite temperature. We also find that the time scales at which the spread complexity and spectral form factor change their behaviour agree with each other and are independent of the chaotic properties of the systems. In the case of spectral complexity, we identify that the key factor determining its saturation value and timescale in chaotic systems is given by minimum energy difference in the theory’s spectrum. This explains observations made in the literature regarding its earlier saturation in chaotic systems compared to their integrable counterparts. We conclude by discussing the properties of the TFD which, we conjecture, make it suitable for probing signatures of chaos in quantum many-body systems. [ABSTRACT FROM AUTHOR]

We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined at t = 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, after t = 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics. [ABSTRACT FROM AUTHOR]

This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the D3/D7 brane configuration. The research explores the non-linear response of the longitudinal current J when subjected to an external electric field E at both zero and finite temperatures. At zero temperature, the study identifies a potential quantum phase transition in the J-E relationship, driven by background parameters the particle mass, and axial gauge potential. This transition is characterized by a unique reconnection phenomenon resulting from the interplay between WSM-like and conventional nonlinear conducting behaviors, indicating a quantum phase transition. Additionally, at non-zero temperatures with dissipation, the system demonstrates first- and second-order phase transitions as the electric field and axial gauge potential are varied. The longitudinal conductivity is used as an order parameter to identify the current-driven phase transition. Numerical analysis reveals critical exponents in this non-equilibrium phase transition that show similarities to mean-field values observed in metallic systems. [ABSTRACT FROM AUTHOR]

We investigate the growth of operator size in the Lindbladian Sachdev-Ye-Kitaev model with q-body interaction terms and linear jump terms at finite dissipation strength. We compute the operator size as well as its distribution numerically at finite q and analytically at large q. With dissipative (productive) jump terms, the size converges to a value smaller (larger) than half the number of Majorana fermions. At weak dissipation, the evolution of operator size displays a quadratic-exponential-plateau behavior. The plateau value is determined by the ratios between the coupling of the interaction and the linear jump term in the large q limit. The operator size distribution remains localized in the finite size region even at late times, contrasting with the unitary case. Moreover, we also derived the time-independent orthogonal basis for operator expansion which exhibits the operator size concentration at finite dissipation. Finally, we observe that the uncertainty relation for operator size growth is saturated at large q, leading to classical dynamics of the operator size growth with dissipation. [ABSTRACT FROM AUTHOR]

The dynamics of first-order phase transitions in strongly coupled systems are relevant in a variety of systems, from heavy ion collisions to the early universe. Holographic theories can be used to model these systems, with fluctuations usually suppressed. In this case the system can come close to a spinodal point where theory and experiments indicate that the behaviour should be similar to a critical point of a second-order phase transition. We study this question using a simple holographic model and confirm that there is critical slowing down and scaling behaviour close to the spinodal point, with precise quantitative estimates. In addition, we determine the start of the scaling regime for the breakdown of quasistatic evolution when the temperature of a thermal bath is slowly decreased across the transition. We also extend the analysis to the dynamics of second-order phase transitions and strong crossovers. [ABSTRACT FROM AUTHOR]

We study the entanglement entropy associated with a holographic RG flow from AdS7 to AdS4 × ℍ3, where ℍ3 is a 3-dimensional hyperbolic manifold with curvature κ. The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c-function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ. We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy. [ABSTRACT FROM AUTHOR]

We investigate the link between quantum position-verification (QPV) and holography established in [1] using holographic quantum error correcting codes as toy models. By inserting the "temporal" scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another. [ABSTRACT FROM AUTHOR]

We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases as due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The Rényi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time. [ABSTRACT FROM AUTHOR]

The rapid development of quantum science and technology is leading us into an era where quantum many-body systems can be comprehended through quantum simulations. Holographic duality, which states gravity and spacetime can emerge from strongly interacting systems, then offers a natural avenue for the experimental study of gravity physics without delving into experimentally infeasible high energies. A prominent example is the simulation of traversable wormholes through the wormhole teleportation protocol, attracting both theoretical and experimental attention. In this work, we develop the theoretical framework for computing the fidelity of wormhole teleportation in N-qubit systems with all-to-all interactions, quantified by mutual information and entanglement negativity. The main technique is the scramblon effective theory, which captures universal out-of-time-order correlations in generic chaotic systems. We clarify that strong couplings between the two systems are essential for simulating the probe limit of semi-classical traversable wormholes using strongly interacting systems with near-maximal chaos. However, the teleportation signal diminishes rapidly when reducing the system size N, requiring a large number of qubits to observe a sharp signature of emergent geometry by simulating the Sachdev-Ye-Kitaev model. This includes both the causal time-order of signals and the asymmetry of the teleportation signal for coupling with different signs. As a comparison, the teleportation signal increases when reducing N in weakly interacting systems. We also analyze the fidelity of the generalized encoding scheme in fermionic string operators. [ABSTRACT FROM AUTHOR]

Pole-skipping refers to the special phenomenon that the pole and the zero of a retarded two-point Green’s function coincide at certain points in momentum space. We study the pole-skipping phenomenon in holographic Green’s functions of boundary operators that are dual to massive p-form fields and the dRGT massive gravitational fields in the AdS black hole background. Pole-skipping points for these systems are computed using the near horizon method. The relation between the pole-skipping points of massive fields and their massless counterparts is revealed. In particular, as the field mass m is varied from zero to non-zero, the pole-skipping phenomenon undergoes an abrupt change with doubled pole-skipping points found in the massive case. This arises from the breaking of gauge invariance due to the mass term and the consequent appearance of more degrees of freedom. We recover the gauge invariance using the Stueckelberg formalism by introducing auxiliary dynamical fields. The extra pole-skipping points are identified to be associated with the Stueckelberg fields. We also observe that, as the mass varies, some pole-skipping points of the wave number q may move from a non-physical region with complex q to a physical region with real q. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we develop the holographic mean field theory for strongly interacting fermion systems. We investigate various types of the symmetry-breakings and their effect on the spectral function. We found analytic expressions of fermion Green’s functions in the probe-limit for all types of tensor order parameter fields. We classified the spectral shapes and singularity types from the analytic Green’s function. We calculated the fermions spectral function in the full backreacted background and then compared it with the analytic results to show the reliability of analytic results in the probe limit. The fact that all the main features of the spectral features in the current condensed matter physics including gaps of s-,p- waves, nodal rings and nodal shells, the flat band of dimension 1,2,3, can be obtained in the absence of the lattice as consequences of the order and symmetry breaking pattern, is a pleaseant surprise.

Abstract We study the non-equilibrium dynamics of two coupled SYK models, conjectured to be holographically dual to an eternal traversable wormhole in AdS2. We consider different periodic drivings of the parameters of the system. We analyze the energy flows in the wormhole and black hole phases of the model as a function of the driving frequency. Our numerical results show a series of resonant frequencies in which the energy absorption and heating are enhanced significantly and the transmission coefficients drop, signalling a closure of the wormhole. These frequencies correspond to part of the conformal tower of states and to the boundary graviton of the dual gravitational theory. Furthermore, we provide evidence supporting the existence of a hot wormhole phase between the black hole and wormhole phases. When driving the strength of the separate SYK terms we find that the transmission can be enhanced by suitably tuning the driving.

Abstract We study the pole-skipping phenomenon within holographic axion theories, a common framework for studying strongly coupled systems with chemical potential (μ) and momentum relaxation (β). Considering the backreaction characterized by μ and β, we encounter coupled equations of motion for the metric, gauge, and axion field, which are classified into spin-0, spin-1, and spin-2 channels. Employing gauge-invariant variables, we systematically address these equations and explore pole-skipping points within each sector using the near-horizon method. Our analysis reveals two classes of pole-skipping points: regular and singular pole-skipping points in which the latter is identified when standard linear differential equations exhibit singularity. Notably, pole-skipping points in the lower-half plane are regular, while those elsewhere are singular. This suggests that the pole-skipping point in the spin-0 channel, associated with quantum chaos, corresponds to a singular pole-skipping point. Additionally, we observe that the pole-skipping momentum, if purely real or imaginary for μ = β = 0, retains this characteristic for μ ≠ 0 and β ≠ 0.

Abstract For any state in a D-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function — a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function can, in general, take on negative values, and the amount of negativity in the Wigner function has an operational meaning as a resource for quantum computation. In this note, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. We introduce the Krylov-Wigner function, i.e., the Wigner function defined with respect to the Krylov basis (with appropriate phases), and show that this choice of basis minimizes the early time growth of Wigner negativity in the large D limit. We take this as evidence that the Krylov basis (with appropriate phases) is ideally suited for a dual, semi-classical description of chaotic quantum dynamics at large D. We also numerically study the time evolution of the Krylov-Wigner function and its negativity in random matrix theory for an initial pure state. We observe that the negativity broadly shows three phases: it rises gradually for a time of O D $$ O\left(\sqrt{D}\right) $$ , then hits a sharp ramp and finally saturates close to its upper bound of D $$ \sqrt{D} $$ .

Abstract We investigate spatially inhomogeneous solutions in a top-down holographic model: the D3/D7 model which provides a holographic description of the chiral phase transition for a finite external magnetic field, chemical potential, and temperature. We numerically find a domain wall (or kink) solution in the three dimensional space, which incorporates between the chiral symmetry broken phase at the spatial infinity, under the homogeneous sources. Along with the inhomogeneity of the chiral condensate, the charge density is also spatially modulated. The modulated charge density and finite magnetic field lead to the chiral edge current close to the domain wall. We explore the dependences of those profiles on the chemical potential and temperature near the first and second order phase transition points. Our results indicate that the inhomogeneous solutions we found are in good agreement with those obtained by the Ginzburg-Landau theory in the vicinity of the transition points.

Abstract We study the linear stability of holographic homogeneous solids (HHS) at finite temperature and in presence of a background shear strain by means of a large scale quasi-normal mode analysis which extends beyond the hydrodynamic limit. We find that mechanical instability can arise either as a result of a complex speed of sound — gradient instability — or of a negative diffusion constant. Surprisingly, the simplest HHS models are linearly stable for arbitrarily large values of the background strain. For more complex HHS, the onset of the diffusive instability always precedes that of the gradient instability, which becomes the dominant destabilizing process only above a critical value of the background shear strain. Finally, we observe that the critical strains for the two instabilities approach each other at low temperatures. We conclude by presenting a phase diagram for HHS as a function of temperature and background shear strain which shows interesting similarities with the physics of superfluids in presence of background superfluid velocity.

Abstract We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm that iteratively generates the Krylov basis can be augmented to treat coherent states associated with the Jacobi group, the semi-direct product of the 3-dimensional real Heisenberg-Weyl group H 1, and the symplectic group, Sp(2, ℝ) ≃ SU(1, 1). Such coherent states are physically realized as squeezed states in, for example, quantum optics [1]. With the Krylov basis for both the SU(1, 1) and Heisenberg-Weyl groups being well understood, their semi-direct product is also partially analytically tractable. We exploit this to benchmark a scheme to numerically compute the Lanczos coefficients which, in principle, generalizes to the more general Jacobi group H n ⋊ Sp(2n, ℝ).