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Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N=2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L)∼L^{1/2} for L sites. For N≥3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L)∼L^{0.57}. This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.

The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.

When a system is swept through a quantum critical point, the quantum Kibble-Zurek mechanism makes universal predictions for quantities such as the number and energy of excitations produced. This mechanism is now being used to obtain critical exponents on emerging quantum computers and emulators, which in some cases can be compared to matrix product state (MPS) numerical studies. However, the mechanism is modified when the divergence of entanglement entropy required for a faithful description of many quantum critical points is not fully captured by the experiment or classical calculation. In this Letter, we study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement, using conformally invariant critical points described approximately by a MPS as an example. We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. Numerically we confirm first that dynamics at finite bond dimension χ is independent of the algorithm chosen, then obtain scaling collapses for sweeps in the transverse field Ising model and the three-state Potts model. Our result establishes the precise role played by entanglement in time-dependent critical phenomena and has direct implications for quantum state preparation and classical simulation of quantum states.

High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this Letter, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a π-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral p-wave superconductor. These results demonstrate the power of Boltzmann machines.

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-1/2 chain falls at low temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in 1+1 dimensions. This Letter aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature T is reduced, we show that the onset of superdiffusion takes place at longer length and timescales ∝1/T. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg S=1/2 chain compound Sr_{2}CuO_{3}, yet calls for new and dedicated experiments.

At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that, at physically relevant parameters, they stabilize a chiral spin liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on a mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In an accompanying paper [T. Schuster et al., Phys. Rev. A 103, AW11986 (2021)PLRAAN2469-9926] we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of ^{40}K^{87}Rb.

In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a cos(2φ) energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive energy levels, and consequently, engineering band pairs with flat spectral gaps can help improve the coherence of the system. We discuss a modified version of a flux qubit that achieves, in principle, no decoherence from charge noise and introduce a flux qutrit that shows a spin-1 Dirac spectrum and is simultaneously quite robust to both charge and flux noise.

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector q to order q^{2}, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al. [Phys. Rev. B 50, 7526 (1994)PRBMDO0163-182910.1103/PhysRevB.50.7526] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics, and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D DDF in the unitary class. We find a critical line at m=0, with an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_{IQH}=2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν_{0}=2.30-2.36 incompatible with ν_{IQH}. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large N theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev model for up to N=60 Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators. Our procedure accurately determines the Lyapunov exponent, λ, across a wide range in temperatures, including in the regime where λ approaches the universal bound, λ=2π/β.

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum e^{3}/h^{2} for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbatrd interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength.

We predict the existence of a Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf Z invariant, a linking number characterizing the (nondriven) Hopf topological insulator. The second invariant is an intrinsically Floquet Z_{2} invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time evolution, subject to a process in which defects at different quasienergies exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0 or π quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.

Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.

The phenomenon of T-linear resistivity commonly observed in a number of strange metals has been widely seen as evidence for the breakdown of the quasiparticle picture of metals. This study shows that a recently discovered H/T scaling relationship in the magnetoresistance of the strange metal BaFe_{2}(As_{1-x}P_{x})_{2} is independent of the relative orientations of current and magnetic field. Rather, its magnitude and form depend only on the orientation of the magnetic field with respect to a single crystallographic axis: the direction perpendicular to the magnetic iron layers. This finding suggests that the magnetotransport scaling does not originate from the conventional averaging or orbital velocity of quasiparticles as they traverse a Fermi surface, but rather from dissipation arising from two-dimensional correlations.

We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a nonuniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics becomes chaotic after a characteristic timescale determined by the interparticle distance and scattering length. The system fails to thermalize over the timescale studied (10^{4} natural units), but the time-averaged ensemble is a stationary state of the hydrodynamic evolution. We close by discussing logical extensions of the results to similar systems of quantum particles.

We explore adiabatic pumping in the presence of a periodic drive, finding a new phase in which the topologically quantized pumped quantity is energy rather than charge. The topological invariant is given by the winding number of the micromotion with respect to time within each cycle, momentum, and adiabatic tuning parameter. We show numerically that this pump is highly robust against both disorder and interactions, breaking down at large values of either in a manner identical to the Thouless charge pump. Finally, we suggest experimental protocols for measuring this phenomenon.

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effective three-dimensional shift current (∼100  μA/V^{2}), larger than has been previously observed in other polar systems. Moreover, we show that the integral of the shift-current tensor is correlated to the large spontaneous effective three-dimensional electric polarization (∼1.9  C/m^{2}). Our calculations indicate that the shift current will be largest in the visible spectrum, suggesting that these monochalcogenides may be promising for polar optoelectronic devices. A Rice-Mele tight-binding model is used to rationalize the shift-current response for these systems, and its dependence on polarization, in general terms with implications for other polar materials.

A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes, depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model and demonstrate universality by adding nonintegrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.

In metallic samples of small enough size and sufficiently strong momentum-conserving scattering, the viscosity of the electron gas can become the dominant process governing transport. In this regime, momentum is a long-lived quantity whose evolution is described by an emergent hydrodynamical theory. Furthermore, breaking time-reversal symmetry leads to the appearance of an odd component to the viscosity called the Hall viscosity, which has attracted considerable attention recently due to its quantized nature in gapped systems but still eludes experimental confirmation. Based on microscopic calculations, we discuss how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields.

The polarization of a material and its response to applied electric and magnetic fields are key solid-state properties with a long history in insulators, although a satisfactory theory required new concepts such as Berry-phase gauge fields. In metals, quantities such as static polarization and the magnetoelectric θ term cease to be well defined. In polar metals, there can be analogous dynamical current responses, which we study in a common theoretical framework. We find that current responses to dynamical strain in polar metals depend on both the first and second Chern forms, related to polarization and magnetoelectricity in insulators as well as the orbital magnetization on the Fermi surface. We provide realistic estimates that predict that the latter contribution will dominate, and we investigate the feasibility of experimental detection of this effect.

We examine localization phenomena associated with generic, high entropy, states of a translation-invariant, one-dimensional spin ladder. At early times, we find slow growth of entanglement entropy consistent with the known phenomenology of many-body localization in disordered, interacting systems. At intermediate times, however, anomalous diffusion sets in, leading to full spin polarization decay on an exponentially activated time scale. We identify a single length scale which parametrically controls both the spin transport times and the apparent divergence of the susceptibility to spin glass ordering. Ultimately, at the latest times, the exponentially slow anomalous diffusion gives way to diffusive thermal behavior. We dub the intermediate dynamical behavior, which persists over many orders of magnitude in time, quasi-many-body localization.

The current density j^{B} induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for α_{ij}^{GME}=j_{i}^{B}/B_{j} in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever the energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), the energy current in Lorentz-invariant theories or the particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call "expansion potentials," expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies nonequilibrium Maxwell relations for the Drude weights. We verify our results via density-matrix renormalization group calculations for the XXZ chain.

Several emergent phenomena and phases in solids arise from configurations of the electronic Berry phase in momentum space that are similar to gauge field configurations in real space such as magnetic monopoles. We show that the momentum-space analogue of the "axion electrodynamics" term E·B plays a fundamental role in a unified theory of Berry-phase contributions to optical gyrotropy in time-reversal invariant materials and the chiral magnetic effect. The Berry-phase mechanism predicts that the rotatory power along the optic axes of a crystal must sum to zero, a constraint beyond that stipulated by point-group symmetry, but observed to high accuracy in classic experimental observations on alpha quartz. Furthermore, the Berry mechanism provides a microscopic basis for the surface conductance at the interface between gyrotropic and nongyrotropic media.

Transport in three-dimensional topological insulators relies on the existence of a spin-momentum locked surface state that encloses the insulating bulk. In this work we show how, in a topological insulator p-n junction, a magnetic field turns this surface state into an electronic Mach-Zehnder interferometer. Transmission of the junction can be tuned from zero to unity, resulting in virtually perfect visibility of the interference pattern, and the reflected and transmitted currents carry opposite spin polarization so that the junction also acts as a spin filter. Our setup therefore realizes a novel and highly tunable spintronic device where the effects of spin-momentum locking in topological insulator surface states can be probed directly in a transport experiment.

Circularly polarized light opens a gap in the Dirac spectrum of graphene and topological insulator (TI) surfaces, thereby inducing a quantum Hall-like phase. We propose to detect the accompanying edge states and their current by the magnetic field they produce. The topological nature of the edge states is reflected in the mean orbital magnetization of the sample, which shows a universal linear dependence as a function of a generalized chemical potential-independent of the driving details and the properties of the material. The proposed protocol overcomes several typically encountered problems in the realization and measurement of Floquet phases, including the destructive effects of phonons and coupled electron baths and provides a way to occupy the induced edge states selectively. We estimate practical experimental parameters and conclude that the magnetization signature of the Floquet topological phase may be detectable with current techniques.

The gapless edge modes of the quantum spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel coupled to a semiconductor quantum dot that is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the quantum spin Hall edge.

The quantum spin Hall insulator is characterized by the presence of gapless helical edge states where the spin of the charge carriers is locked to their direction of motion. In order to probe the properties of the edge modes, we propose a design of a tunable quantum impurity realized by a local gate under an external magnetic field. Using the integrability of the impurity model, the conductance is computed for arbitrary interactions, temperatures and voltages, including the effect of Fermi liquid leads. The result can be used to infer the strength of interactions from transport experiments.

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.

We propose an easily implemented approach to study time-dependent correlation functions of one-dimensional systems at finite-temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long-time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero--and thus transport is dissipationless--everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.

Weak topological insulators have an even number of Dirac cones in their surface spectrum and are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states; rather, the presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form.

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.

We investigate the band dispersion and the spin texture of topologically protected surface states in the bulk topological insulators Bi2Se3 and Bi2Te3 by first-principles methods. Strong spin-orbit entanglement in these materials reduces the spin polarization of the surface states to ∼50% in both cases; this reduction is absent in simple models but of important implications to essentially any spintronic application. We propose a way of controlling the magnitude of spin polarization associated with a charge current in thin films of topological insulators by means of an external electric field. The proposed dual-gate device configuration provides new possibilities for electrical control of spin.

Several small-band-gap semiconductors are now known to protect metallic surface states as a consequence of the topology of the bulk electron wave functions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi₂Te₃ and Bi₂Se₃, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts that the tunable hybridization-induced band gap leads to increased thermoelectric performance at low temperatures. Beyond simple diffusive transport, the conductivity shows a crossover from the spin-orbit-induced antilocalization at a single surface to ordinary localization.

A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi2Se3 nanowires [Peng, Nature Mater. 9, 225 (2010)] where conductance was found to oscillate as a function of magnetic flux ϕ through the wire, with a period of one flux quantum ϕ0=h/e and maximum conductance at zero flux. This seemingly agrees neither with diffusive theory, which would predict a period of half a flux quantum, nor with ballistic theory, which in the simplest form predicts a period of ϕ0 but a minimum at zero flux due to a nontrivial Berry phase in topological insulators. We show how h/e and h/2e flux oscillations of the conductance depend on doping and disorder strength, provide a possible explanation for the experiments, and discuss further experiments that could verify the theory.

The photocurrent in an optically active metal is known to contain a component that switches sign with the helicity of the incident radiation. At low frequencies, this current depends on the orbital Berry phase of the Bloch electrons via the "anomalous velocity" of Karplus and Luttinger. We consider quantum wells in which the parent material, such as GaAs, is not optically active and the relevant Berry phase only arises as a result of quantum confinement. Using an envelope approximation that is supported by numerical tight-binding results, it is shown that the Berry-phase contribution is determined for realistic wells by a cubic Berry phase intrinsic to the bulk material, the well width, and the well direction. These results for the Berry-phase effect suggest that it may already have been observed in quantum well experiments.

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a novel exotic quantum state which we propose to call "topological exciton condensate" (TEC). This TEC is similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. It exhibits a host of unusual properties including a stable zero mode and a fractional charge +/-e/2 carried by a singly quantized vortex in the TEC order parameter.

Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling theta, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability theta is the same parameter that appears in the "axion electrodynamics" Lagrangian DeltaL_{EM}=(thetae;{2}/2pih)E.B, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator (theta=pi). We compute theta for a simple model that accesses the topological insulator and discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wave function and defines the 3D topological insulator, like the integer quantum Hall effect, in terms of a topological ground-state response function.

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.

We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor condensates. In addition to the familiar triangular lattice predicted by Tkachenko for 4He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aperiodic vortex structure. Finally, we compute the renormalization of the ratio of the spin and charge stiffnesses from thermal fluctuations using a nonlinear sigma model analysis.

We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.

Systems near to quantum critical points show universal scaling in response to external probes. We consider whether this scaling is reflected in their out-of-equilibrium fluctuations. We study current noise in the metallic state at the z=1 quantum critical point between a superconductor and an insulator in two dimensions. Using a Boltzmann-Langevin approach within a 1/N expansion, we show that the current noise obeys a universal scaling form S_{j}=TPhi[T/T_{eff}(E)], with T_{eff} proportional, variantsqrt[E]. This treatment recovers Johnson noise in thermal equilibrium and S_{j} proportional, variantsqrt[E] at strong electric fields. The latter differs significantly from both the shot noise in conventional metals (diffusive Fermi liquids) and the free carrier result, due to strong correlations between the critical bosonic excitations. Current-noise measurements could therefore help clarify the physics of the destruction of superconductivity in thin film superconductors.