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A set of universal quantum gates is a vital part of the theory of quantum computing, but is absent in the developing theory of Relativistic Quantum Information (RQI). Yet, the Unruh--DeWitt (UDW) detector formalism can be elevated to unitary gates between qubits and quantum fields and has allowed RQI applications in quantum Shannon theory, such as mutual information, coherent information, and quantum capacity in field-mediated quantum channels. Recently, experimental realizations of UDW-style qubits have been proposed in two-dimensional quantum materials, but their value as a quantum technology, including quantum communication and computation, is not yet clear, especially since fields introduce many avenues for decoherence. We introduce controlled-unitary UDW logic gates between qubit and field that are comparable to the two-qubit CNOT gate. We then extend this formalism to demonstrate Quantum State Transfer (QST) (two CNOT gates) and SWAP (three CNOT gates) channels. We illustrate the performance of these quantum operation gates with the diamond distance, a measure of distinguishability between quantum channels. Distinguishability measures like diamond distance allow for a rigorous comparison between field-mediated transduction through UDW detectors and local quantum mechanical operations and so quantify the performance of UDW detectors in quantum technological applications. Using the controlled-unitary qubit-field interactions we define an exact form of the CNOT gate. With this technique we also define quantum field-mediated single qubit operations associated with the Hadamard $H$, the $S$, and $T$ gates. Thus, UDW detectors in simple settings enable a collection of gates known to provide universal quantum computing., Comment: 17 pages, 11 figures, 4 tables

The entanglement-induced barren plateau is an exponential vanishing of the parameter gradients with system size that limits the practical application of variational quantum algorithms(VQA). A landscape transition from barren plateau to no-barren plateau was recently observed in monitored quantum circuits, hypothesized to coincide with the measurement-induced phase transition (MIPT) that separates the area-law states from the volume-law states. We argue from an information theory perspective that these are different transitions. This hypothesis is supported by a numerical study that includes cost-gradient variances, visualizations of the optimization runs and cost-landscape, and a quantum-classical channel mutual information measure. The results are evidence for a universal measurement-induced landscape transition (MILT) at $p_c^{\text{MILT}} \approx 0.2 < p_c^{\text{MIPT}}$ and that throughout $0

Unruh--DeWitt (UDW) detectors implemented as UDW quantum gates provide a framework for evaluating quantum Shannon theory properties of qubit-field systems. UDW quantum channels consist of qubits encoding/decoding quantum information onto/off of quantum fields. With the controlled unitary structure of UDW gates, the encoding/decoding process happens on the diagonals of the coherent state density matrix describing the field. However, given the non-orthogonality of coherent states the output of UDW channels consists of unwanted states and unwanted mixing of states that lower the channel capacity. In idealized models, these appear in the off-diagonals and diagonals of the field's density matrix in the coherent state basis. For this reason, we show that UDW quantum channels have an unexpected representation as certain bosonic dephasing channels with dephasing parameters captured by a combination of the coupling, smearing, and switching functions of the UDW detector model. We demonstrate the unexpected consequence that a larger dephasing parameter results in higher channel capacity and helps alleviate unwanted state mixing. We illustrate these properties through two examples: inserting an additional ideal dephasing channel into the quantum channel and inserting cross-talk noise via a third UDW gate. Remarkably, the cross-talk noise channel qualitatively improves a lower bound on the quantum capacity suggesting UDW gates will have unexpected performance improvements if realized in condensed matter experiments., Comment: 8 pages, 3 figures

$\alpha$-RuCl3 is a magnetic insulator exhibiting quantum spin liquid phases possibly found in the Kitaev honeycomb model. Much of the effort towards determining Hamiltonian parameters has focused on low magnetic field ordered phases. We study this problem in the high magnetic field limit where mean-field theory is better justified. We do so by machine-learning model parameters from over 200,000 low dimensional data points by combining available magnetization, torque, and torsion data sets. Our machine, an artificial neural network-mean-field theory (ANN-MFT) encoder, maps thermodynamic conditions (temperature and field vector) to model parameters via a fully connected time-reversal covariant (equivariant) neural network and then predicts observable values using mean-field theory. To train the machine, we use PyTorch to enable backpropagation through mean-field theory with a pure PyTorch implementation of the Newton-Raphson method. The results at $20$ K and $34.5$ T are consistent with other parameter inference studies in the literature at low magnetic field but strikingly have magnitudes that scale with temperature from 1.3 K up to 80 K in the $34.5-60$ T range. We conclude that the data presents physics beyond the scope of the mean-field theory and that strong interactions dominate the physics of $\alpha$-RuCl$_3$ up to field strengths of at least 60 Tesla., Comment: 12 pages, 8 figures, 2 code listings

Quantum computers and simulators promise to enable the study of strongly correlated quantum systems. Yet, surprisingly, it is hard for them to compute ground states. They can, however, efficiently compute the dynamics of closed quantum systems. We propose a method to study the quantum thermodynamics of strongly correlated electrons from quantum dynamics. We define time-averaged classical shadows (TACS) and prove it is a classical shadow(CS) of the von Neumann ensemble, the time-averaged density matrix. We then show that the diffusion maps, an unsupervised machine learning algorithm, can efficiently learn the phase diagram and phase transition of the one-dimensional transverse field Ising model both for ground states using CS \emph{and state trajectories} using TACS. It does so from state trajectories by learning features that appear to be susceptibility and entropy from a total of 90,000 shots taken along a path in the microcanonical phase diagram. Our results suggest a low number of shots from quantum simulators can produce quantum thermodynamic data with a quantum advantage.

The Unruh-DeWitt particle detector model has found success in demonstrating quantum information channels with non-zero channel capacity between qubits and quantum fields. These detector models provide the necessary framework for experimentally realizable Unruh-DeWitt Quantum Computers with near-perfect channel capacity. We propose spin qubits with gate-controlled coupling to Luttinger liquids as a laboratory setting for Unruh-DeWitt detectors and general design constraints that underpin their feasibility in this and other settings. We also present several experimental scenarios including graphene ribbons, edges states in the quantum spin Hall phase of HgTe quantum wells, and the recently discovered quantum anomalous Hall phase in transition metal dichalcogenides. Theoretically, through bosonization, we show that Unruh-DeWitt detectors can carry out Quantum Computations and when they can make perfect quantum communication channels between qubits via the Luttinger liquid. Our results point the way toward an all-to-all connected solid state quantum computer and the experimental study of quantum information in quantum fields via condensed matter physics., Comment: 12 pages, 7 figures, 1 table, version 3

Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices involved in each problem. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincar\'e-Hopf index. It turns out, because of the mathematical similarity, this topological index shows a way to approach supersymmetric quantum theory from classical mechanics. Using this mathematical similarity, we establish a topological connection between isostatic mechanical metamaterials and supersymmetric quantum systems, such as electrons coupled to phonons in metals and superconductors. Firstly, we define $Q_{net}$ for an isostatic mechanical system that counts the minimum number of zero-energy configurations. Secondly, we write a supersymmetric Hamiltonian that describes a metal or a superconductor interacting with anharmonic phonons. This Hamiltonian has a Witten index, a topological invariant that captures the balance of bosonic and fermionic zero-energy states. We are able to connect these two systems by showing that $Q_{net}=W$ under very general conditions. Our result shows that (1) classical metamaterials can be used to study the topology of interacting quantum systems with aid of supersymmetry, and (2) with fine-tuning between anharmonicity of phonons and couplings among Majorana fermions and phonons, it is possible to realize such a supersymmetric quantum system that shares the same topology as classical mechanical systems.

Topological frustration (or topological mechanics) is the existence of classical zero modes that are robust to many but not all distortions of the Hamiltonian. It arises naturally from locality in systems whose interactions form a set of constraints such as in geometrically frustrated magnets and balls and springs metamaterials. For a magnet whose classical limit exhibits topological frustration, an important question is what happens to this topology when the degrees of freedom are quantized and whether such frustration could lead to exotic quantum phases of matter like a spin liquid. We answer these questions for a geometrically frustrated spin ladder model. It has the feature of having infinitely many conserved quantities that aid the solution. We find classical zero modes all get lifted by quantum fluctuations and the system is left with a unique rung singlet ground state -- a trivial quantum spin liquid. Moreover, we find low-energy eigenstates corresponding to known symmetry protected topological (SPT) ground states, and a special role of $SU(2)$ symmetry, that it demands the existence of extra dimensions of classical zero modes -- the phenomena we call symmetry-enriched topological frustration (SETF). These results suggest small violations of the conservation laws in the nearly SETF regime could lead to quantum scars. We further study a two-dimensional bilayer triangular lattice model and find a similar SETF phenomena which also leads to suppressed low-energy topological eigenstates in the quantum regime. These results suggest that in the absence of magnetic order, classical topological frustration manifests at finite spin as asymptotically low energy modes with support for exotic quantum phenomena.

In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons, and fermions defined by local rules. Here we apply it to find connections between bosonic and fermionic lattice models in the realm of condensed matter physics and uncover a novel 5-fold way topology it demands in these systems. At the single-particle level, our connections pair a bosonic and fermionic lattice model, either describing the hopping of number-conserving particles or local couplings between fermion parity-conserving particles. The pair are isospectral except for zero modes, such as flat bands, quadratic band touchings, and nexus points, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences. Notably, in this framework, the supercharge operator that generates SUSY is Hermitian and can itself be interpreted as a hopping Hamiltonian on a bipartite lattice, a feature that enables the discovery of materials or model lattices hosting the SUSY partners. To illustrate the power of SUSY, we present 16 use cases of SUSY, that span topics including frustrated magnets, Kitaev spin liquids, and topological superconductors, the majority of which turn out to provide insights into the discovery and design of flat bands and topological materials., Comment: 39 pages, 30 figures

Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near-term. We propose a scheme to simulate and characterize many-body Floquetsystems hosting a rich variety of phases that operates with a shallow depth circuit. Starting from a "clean" periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasi-periodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting the time averaged properties of the many-body integrals of motion, the phase structure can then be probed using random measurements. This approach avoids the need to compute the ground state and operates at finite energy density. We numerically demonstrate this scheme with a simulation of the Floquet Ising model of time-crystals and present results clearly distinguishing different Floquet phases in the absence of quasi-periodicity in the circuit parameters. Our results pave the way for mapping phase diagrams of exotic systems on near-term quantum devices., Comment: 7 pages, 7 figures

Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites (12 qubits) by using an interpretable, adaptive variational quantum eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this algorithm builds a system-specific ansatz by adding an optimal gate built from one-body or two-body fermionic operators at each step. We show this adaptive method outperforms the non-adaptive counterpart in terms of fewer variational parameters, short gate depth, and scaling with the system size. The fidelity and energy of the prepared state appear to improve asymptotically with ansatz depth. We also demonstrate the application of adaptive variational methods by preparing excited states and Green functions using a proposed ADAPT-SSVQE algorithm. Lower depth, asymptotic convergence, noise tolerance of a variational approach, and a highly controllable, system-specific ansatz make the adaptive variational methods particularly well-suited for NISQ devices.

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological indices which accommodates non-linear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of the Poincare-Hopf index, that features the topological invariant of non-linear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected non-linear ZMs in the future.

Metal-organic frameworks (MOFs) are nanoporous compounds composed of metal ions and organic linkers. MOFs play an important role in industrial applications such as gas separation, gas purification, and electrolytic catalysis. Important MOF properties such as potential energy are currently computed via techniques such as density functional theory (DFT). Although DFT provides accurate results, it is computationally costly. We propose a machine learning approach for estimating the potential energy of candidate MOFs, decomposing it into separate pair-wise atomic interactions using a graph neural network. Such a technique will allow high-throughput screening of candidates MOFs. We also generate a database of 50,000 spatial configurations and high-quality potential energy values using DFT., Comment: Accepted for presentation at the Machine Learning for Molecules Workshop at NeurIPS 2020

Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long range magnetic order in the family of pyrochlore iridates, R$_{2}$Ir$_{2}$O$_{7}$ (R = lanthanide)$^{1}$. As a consequence, Pr$_{2}$Ir$_{2}$O$_{7}$ lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits a diverse array of complex phenomena including Kondo effect, biquadratic band structure, metallic spin-liquid (MSL), and anomalous Hall effect$^{2-5}$. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning K-means clustering analysis, density functional theory, and theoretical modeling, we probe the local electronic states in single crystal of Pr$_{2}$Ir$_{2}$O$_{7}$ and discover an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. Remarkably, the spatial nanoscale patterns display a correlation-driven fractal geometry with power-law behavior extended over two and a half decades, consistent with being in proximity to a critical point. Our discovery reveals a new nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration., Comment: Nature Communications (in press)

The CuO$_2$ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E|<$\Delta^*$, where $\Delta^*$ is the pseudogap energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q density-wave (DW) state and a Q=0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken symmetry states to be visualized simultaneously. Using this approach, we show that, even though their reported ordering temperatures T$_{DW}$ and T$_{NE}$ are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the pseudogap energy $\Delta^*$. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi-surface), while the observed pseudogap opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries can be understood as the natural consequence of a vestigial nematic state , within the pseudogap phase of Bi$_2$Sr$_2$CaCu$_2$O$_8$.

Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of isotropic and anisotropic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than nematic order detected from Bragg peaks which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe2As2, and it predicts nematic symmetry breaking with 99% confidence (probability 0.99), in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking., Comment: 10 pages, 9 figures

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples we discuss mechanical analogues of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature., Comment: 8 pages, 6 figures

We study the relationship between the physics of topology and zero modes in frustrated systems and metama- terials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kind of zero modes in form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple question: are the robust features of frustration topologically protected and if so can we classify different types of frustration using topology? In answering these questions we invoke the tools of topological mechanics to identify the key agent at play, namely the rigidity matrix, which is a non-Hermitian matrix and decides the topology of spin-wave zero modes in a frustrated magnet or phonon modes in metamaterials. Further developments of the theory rely on combining the recent developments in our understanding of Maxwell constraint counting and generalizing the ten-fold way classification of Hermitian matrices to non-Hermitian matrices. The result is a three-fold way classification for each Maxwell counting index. We illustrate the clas- sification by demonstrating the existence of a new vortex-like invariant for real rigidity matrices using random matrices and through example frustrated spin models. So by classifying all the rigidity matrices, we answer the question of the origin of frustration (i.e. zero modes in the form of accidental degeneracy) in a wide class of frustrated magnets and metamaterials by linking it to topological invariants., Comment: 18 pages, 10 figures

A mysterious incoherent metallic (IM) normal state with $T$-linear resistivity is ubiquitous among strongly correlated superconductors. Recent progress with microscopic models exhibiting IM transport has presented the opportunity for us to study new models that exhibit direct transitions into a superconducting state out of IM states within the framework of connected Sachdev-Ye-Kitaev (SYK) "quantum dots". Here local SYK interactions within a dot produce IM transport in the normal state, while local attractive interactions drive superconductivity. Through explicit calculations, we find two features of superconductivity arising from an IM normal state: First, despite the absence of quasiparticles in the normal state, the superconducting state still exhibits coherent superfluid transport. Second, the non-quasiparticle nature of the IM Green's functions produces a large enhancement in the ratio of the zero-temperature superconducting gap $\Delta$ and transition temperature $T_{sc}$, $2\Delta/T_{sc}$, with respect to its BCS value of $3.53$., Comment: 4 pages, 3 figures + references + appendices. Added analysis of superconducting transition

When very high magnetic fields suppress the superconductivity in underdoped cuprates, an exceptional new electronic phase appears. It supports remarkable and unexplained quantum oscillations and exhibits an unidentified density wave (DW) state. Although generally referred to as a "charge" density wave (CDW) because of the observed charge density modulations, theory indicates that this could actually be the far more elusive electron-pair density wave state (PDW). To search for evidence of a field-induced PDW in cuprates, we visualize the modulations in the density of electronic states $N(\bf{r})$ within the halo surrounding Bi$_2$Sr$_2$CaCu$_2$O$_8$ vortex cores. This reveals multiple signatures of a field-induced PDW, including two sets of $N(\bf{r})$ modulations occurring at wavevectors $\bf{Q}_P$ and $2\bf{Q}_P$, both having predominantly $s$-symmetry form factors, the amplitude of the latter decaying twice as rapidly as the former, along with induced energy-gap modulations at $\bf{Q}_P$ . Such a microscopic phenomenology is in detailed agreement with theory for a field-induced primary PDW that generates secondary CDWs within the vortex halo. These data indicate that the fundamental state generated by increasing magnetic fields from the underdoped cuprate superconducting phase is actually a PDW with approximately eight CuO$_2$ unit-cell periodicity ($\lambda = 8a_0$) and predominantly $d$-symmetry form factor.

Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a generalized "spin origami" two-dimensional mechanical sheet. Some such anisotropic spin systems, including Cs2ZrCu3F12, map onto flat origami sheets, possessing extensive degeneracy similar to isotropic systems. Others, such as Cs2CeCu3F12, can be mapped onto sheets with non-zero Gaussian curvature, leading to more mechanically stable corrugated surfaces. Remarkably, even such distortions do not always lift the entire degeneracy, instead permitting a large but sub-extensive space of zero-energy modes. We show that for Cs2CeCu3F12, due to an additional point group symmetry associated with structure, these modes are 'Dirac' line nodes with a double degeneracy protected by a topological invariant. The existence of mechanical analogs thus serves to identify and explicate the robust degeneracy of the spin systems., Comment: 5 pages, 4 figures

We found new two-dimensional (2D) quantum (S=1/2) antiferromagnetic systems: CuRE2Ge2O8 (RE=Y and La). According to our analysis of high-resolution X-ray and neutron diffraction experiments, the Cu-network of CuRE2Ge2O8 (RE=Y and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular b-axis. Our bulk characterizations from 0.08 to 400 K show that they undergo a long-range order at 0.51(1) and 1.09(4) K for the Y and La systems, respectively. Interestingly, they also exhibit field induced phase transitions. For theoretical understanding, we carried out the density functional theory (DFT) band calculations to find that they are typical charge-transfer-type insulators with a gap of Eg = 2 eV. Taken together, our observations make CuRE2Ge2O8 (RE=Y and La) additional examples of low-dimensional quantum spin triangular antiferromagnets with the low-temperature magnetic ordering., Comment: 15 pages, 6 figures, and 1 table

We propose an experimental protocol for using cold atoms to create and probe quantum dimer models, thereby exploring the Pauling-Anderson vision of a macroscopic collection of resonating bonds. This process can allow the study of exotic crystalline phases, fractionalization, topological spin liquids, and the relationship between resonating dimers and superconductivity subjects which have been challenging to address in solid-state experiments. Our key technical development is considering the action of an off-resonant photoassociation laser on large spin atoms localized at the sites of a deep optical lattice. The resulting superexchange interaction favors nearest-neighbor singlets. We derive an effective Hamiltonian in terms of these dimer degrees of freedom, finding that it is similar to well-known quantum dimer models, which boast a rich variety of valence bond crystal and spin liquid phases. We numerically study the ground state, explain how to tune the parameters, and develop a protocol to directly measure the dimers and their resonating patterns., Comment: 13 pages including references and appendices, 8 figures (including supplementary materials); Included fermionic species as candidates to simulate the quantum dimer model; Reorganized manuscript to improve readability; Added numerical estimates of energy scales in our system; Conclusions unchanged

Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting superconducting order parameter to be nodeless $s\pm d$-wave within each domain. Further we show that orbital dependent Hund's coupling can readily capture observed gap anisotropy. Our prediction calls for inelastic neutron scattering in a detwinned sample., Comment: revised version, 6+8 pages, 4+7 figures

Chemical substitution plays a key role in controlling the electronic and magnetic properties of complex materials. For instance, in EuO, carrier doping can induce a spin-polarized metallic state, colossal magnetoresistance, and significantly enhance the Curie temperature. Here, we employ a combination of molecular-beam epitaxy, angle-resolved photoemission spectroscopy, and an effective model calculation to investigate and understand how semi-localized states evolve in lightly electron doped Eu$_{1-x}$Gd$_{x}$O above the ferromagnetic Curie temperature. Our studies reveal a characteristic length scale for the spatial extent of the donor wavefunctions which remains constant as a function of doping, consistent with recent tunneling studies of doped EuO. Our work sheds light on the nature of the semiconductor-to-metal transition in Eu$_{1-x}$Gd$_{x}$O and should be generally applicable for doped complex oxides.

Half-filled Landau levels form a zoo of strongly correlated phases. These include non-Fermi liquids (NFL), fractional quantum Hall (FQH) states, nematic phases, and FQH nematic phases. This diversity poses the question: what keeps the balance between the seemingly unrelated phases? The answer is elusive because the Halperin-Lee-Read (HLR) description that offers a natural departure point is inherent strongly coupled. But the observed nematic phases suggest nematic fluctuations play an important role. To study this possibility, we apply a recently formulated controlled double expansion approach in large-$N$ composite fermion flavors and small $\epsilon$ non-analytic bosonic action to the case with both gauge and nematic boson fluctuations. In the vicinity of a nematic quantum critical line (NQCL), we find that depending on the amount of screening of the gauge- and nematic-mediated interactions controlled by $\epsilon$'s, the RG flow points to all four mentioned correlated phases. When pairing preempts the nematic phase, NFL behavior is possible at temperatures above the pairing transition. We conclude by discussing measurements at low tilt angles which could reveal the stabilization of the FQH phase by nematic fluctuations.

The original proposal to achieve superconductivity by starting from a quantum spin-liquid (QSL) and doping it with charge carriers, as proposed by Anderson in 1987, has yet to be realized. Here we propose an alternative strategy: use a QSL as a substrate for heterostructure growth of metallic films to design exotic superconductors. By spatially separating the two key ingredients of superconductivity, i.e., charge carriers (metal) and pairing interaction (QSL), the proposed setup naturally lands on the parameter regime conducive to a controlled theoretical prediction. Moreover, the proposed setup allows us to "customize" electron-electron interaction imprinted on the metallic layer. The QSL material of our choice is quantum spin ice well-known for its emergent gauge-field description of spin frustration. Assuming the metallic layer forms an isotropic single Fermi pocket, we predict that the coupling between the emergent gauge-field and the electrons of the metallic layer will drive topological odd-parity pairing. We further present guiding principles for materializing the suitable heterostructure using ab initio calculations and describe the band structure we predict for the case of Y$_2$Sn$_{2-x}$Sb$_x$O$_7$ grown on the (111) surface of Pr$_2$Zr$_2$O$_7$. Using this microscopic information, we predict topological odd-parity superconductivity at a few Kelvin in this heterostructure, which is comparable to the $T_c$ of the only other confirmed odd-parity superconductor Sr$_2$RuO$_4$., Comment: 13 papers, 3 figures + 30 pages of supplemental material

Order by disorder is a decision making process for frustrated systems but often leads to simple answers. We study order by disorder in the kagome Kondo model known for its complexity seeking rich decision making capabilities. At half filling and large Kondo coupling to hopping ratio $J_K/t$, the full manifold of 120$^o$ kagome ground states are degenerate at second order in $t/J_K$. We show this degeneracy lifts at sixth order when a fermion can hop around a hexagon and feel the Berry flux induced by a given spin texture. Using Monte-Carlo we then seek the ground state of this sixth order Hamiltonian and find in a 4x4 unit cell system that a co-planar 2x4 unit cell order is selected over the $\sqrt{3}\times\sqrt{3}$, $q=0$ and cuboc1 states, a result that survives even in the thermodynamic limit. This state is selected for its SU(2) flux properties induced by the spin texture and is analogous to the integer quantum Hall effect. Given the existence of numerous quantum Hall plateaus in other systems, the existence of this 2x4 unit cell state suggests that complex decision making is possible on the manifold of 120$^o$ states and achievable in different kagome-Kondo models.

Mott insulating ultracold gases posses a unique whole-atom exchange interaction which enables large quantum fluctuations between the Zeeman sublevels of each atom. By strengthening this interaction---either through the use of large-spin atoms, or by tuning the particle-particle interactions via optical Feshbach resonance---one may enhance fluctuations and facilitate the appearance of the long sought-after quantum spin liquid phase---all in the highly tunable environment of cold atoms. To illustrate the relationship between the spin magnitude, interaction strength, and resulting magnetic phases, we present and solve a mean field theory for bosons optically confined to the one particle-per-site Mott state, using both analytic and numerical methods. We find on a square lattice with bosons of hyperfine spin $f>2$, that making the repulsive s-wave scattering length through the singlet channel small---relative to the higher-order scattering channels---accesses a short-range resonating valence bond (s-RVB) spin liquid phase., Comment: 7 pages, 4 figures

I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle) I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest neighbor antiferromagnets, and the $J_2 = J_1/2$ square lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collections of models. Thus, a solid state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials., Comment: 16 pages, 7 figures

Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group calculation for the problem of two dimensional superconductors with point nodes, we show that quantum critical fluctuations associated with point group symmetry reduction result in non-universal logarithmic corrections to the $T$-dependence of the PD. The resulting apparent power law depends on the bare velocity anisotropy ratio. We then compare our results to data sets from two distinct nodal superconductors: YBa$_2$Cu$_3$O$_{6.95}$ and CeCoIn$_5$. Considering all symmetry-lowering possibilities of the point group of interest, $C_{4v}$, we find our results to be remarkably consistent with YBa$_2$Cu$_3$O$_{6.95}$ being near vertical nematic QCP, and CeCoIn$_5$ being near diagonal nematic QCP. Our results motivate search for diagonal nematic fluctuations in CeCoIn$_5$., Comment: Published version, 12 pages, 3 figures, 1 table

We consider the potential for novel forms of magnetism arising from the subtle interplay between electrons and spins in the under-screened kagome Kondo lattice model. At weak coupling, we show that incommensurate non-coplanar multi-wave vector magnetic orders arise at nearly all fillings and that this results from Fermi surface effects that introduces competing interactions between the spins. At strong coupling, we find that such complex order survives near half filling despite the presence of ferromagnetism at all other fillings. We show this arises due to state selection among a massive degeneracy of states at infinite coupling. Finally, we show that at intermediate filling, only commensurate orders seem to survive. But these orders still include non-coplanar magnetism. So, the mere presence of both local moments and itinerant electrons enables complex orders to form unlike any currently observed in kagome materials., Comment: 4.5 pages + 7.5 pages Supplementary Information. 10 figures

Recent experimental discoveries have brought a diverse set of broken symmetry states to the center stage of research on cuprate superconductors. Here, we focus on a thematic understanding of the diverse phenomenology by exploring a strong-coupling mechanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a variational study of a three-band model of the CuO$_2$ plane with Kondo-type exchange couplings between doped oxygen holes and classical copper spins. Two main findings from this strong-coupling multi-band perspective are 1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order and isotropic phases are all accessible microscopically within the model, 2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. These results indicate that the diverse phenomenology of broken-symmetry states in hole-doped antiferromagnetic charge-transfer insulators may indeed arise from hole-doped frustration of antiferromagnetism.

The spinon continues to be an elusive elementary excitation of frustrated antiferromagnets. To solidify evidence for its existence, we address the question of what will be the Angle Resolved Photoemission Spectroscopy (ARPES) signatures of single crystal samples of Herbertsmithite assuming it is described by the Dirac spin liquid state. In particular, we show that the electron spectral function will have a linear in energy dependence near specific wave vectors and that this dependence is expected even after fluctuations to the mean field values are taken into account. Observation of this unique signature in ARPES will provide very strong evidence for the existence of spinons in greater than one dimension., Comment: 10 pages

The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to $Z_2$. Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-Paratacamite suggesting it may already be realized in these materials., Comment: 4+ pages, 3 figures

Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting fluctuating stripes. We also present a microscopic mechanism of IUC nematic order driven by on-site and near-neighbor repulsions. Finally we discuss open questions in the context of these results., Comment: 26 pages, 10 figures. To be published in Physica C

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research. By studying the Bragg peaks in Fourier transforms of electronic structure images, and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such Bragg-peak Fourier analysis. Exemplary of this challenge is the high temperature superconductor Bi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2% (2pi) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane. Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for Bragg-peak Fourier analysis of intra-unit-cell symmetry., Comment: Main article + figures, Supplementary Data + Figures; accepted to New Journal of Physics

One of the key motivations for the development of atomically resolved spectroscopic imaging STM (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E|={\Delta}0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k=\pm({\pi}/a0,0) to k=\pm(0, {\pi}/a0). In both the dSC and PG phases, the only broken symmetries detected in the |E|\leq {\Delta}0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E| {\Delta}1 which is associated conventionally with the 'antinodal' states near k=\pm({\pi}/a0,0) and k=\pm(0, {\pi}/a0). We find that these states break the 90o-rotational (C4) symmetry of electronic structure within CuO2 unit cells, at least down to 180o rotational (C2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C4 symmetry breaking coexists at |E| {\Delta}1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The properties of these two classes of |E| {\Delta}1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E| {\Delta}1 and |E|\leq{\Delta}0, and to understand how this impacts the electronic phase diagram and the mechanism of high-Tc superconductivity, represents one of a key challenges for cuprate studies., Comment: 45 pages, 12 figures