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The orbital Hall effect (OHE) typically is evaluated using an intuitive approach based on semiclassical considerations. Here we provide a full quantum mechanical evaluation of the orbital current, including all matrix elements of the position operator. We recover previous results and find an additional quantum correction due to the non-commutativity of the position and velocity operators. We evaluate the full OHE for the topological antiferromagnet CuMnAs showing that the quantum correction dominates the response and changes its sign. We discuss implications for experiment., Comment: Submitted to Phys.Rev.Lett

Orbitronics harnesses non-equilibrium densities and flows of electrons orbital angular momentum (OAM). Although the OAM must be long lived to be useful in information processing, the mechanisms leading to OAM non-conservation remain unknown. Here we show that an electric field induces an intrinsic torque on the OAM mediated by the quantum metric tensor, without spin-orbit coupling or magnetic fields. The torque vanishes in pseudospin-1/2 systems with particle-hole symmetry but is nonzero in the presence of nontrivial textures. We discuss implications for topological materials and strategies for experimental observation.

The in-plane and out-of-plane superconducting stiffness of LSCO rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio $\alpha$ of interplane over intraplane superconducting stiffnesses. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature $T_{\rm c}$, and the out of-plane stiffness appears to vanish below $T_{\rm c}$ by a temperature shift of order $\alpha L_a/\xi^\parallel$, where $L_a/\xi^\parallel$ is the sample's width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by $\alpha=4.1\times 10^{-5}$ near $T_{\rm c}$, which is significantly lower than its previously measured value near zero temperature.

We generalize the recent work of Shibata and Katsura, who considered a S=1/2 chain with alternating XX and YY couplings in the presence of dephasing, the dynamics of which are described by the GKLS master equation. Their model is equivalent to a non-Hermitian system described by the Kitaev formulation in terms of a single Majorana species hopping on a two-leg ladder in the presence of a nondynamical Z_2 gauge field. Our generalization involves Dirac gamma matrix `spin' operators on the square lattice, and maps onto a non-Hermitian square lattice bilayer which is also Kitaev-solvable. We describe the exponentially many non-equilibrium steady states in this model. We identify how the spin degrees of freedom can be accounted for in the 2d model in terms of the gauge-invariant quantities and then proceed to study the Liouvillian spectrum. We use a genetic algorithm to estimate the Liouvillian gap and the first decay modes for large system sizes. We observe a transition in the first decay modes, similar to that found by Shibata and Katsura. The results we obtain are consistent with a perturbative analysis for small and large values of the dissipation strength., Comment: 19 pages, 23 figures, v2

Band-touching Weyl points in Weyl semimetals give rise to many novel characteristics, one of which the presence of surface Fermi-arc states that is topologically protected. The number of such states can be computed by the Chern numbers at different momentum slices, which fluctuates with changing momentum and depends on the distribution of Weyl points in the Brillouin zone. For realistic systems, it may be difficult to locate the momenta at which these Weyl points and Fermi-arc states appear. Therefore, we extend the analysis of a parametric random matrix model proposed by Walker and Wilkinson to find the statistics of their distributions. Our numerical data shows that Weyl points with opposite polarities are short range correlated, and the Chern number fluctuation only grows linearly for a limited momentum difference before it saturates. We also find that the saturation value scales with the total number of bands. We then compute the short-range correlation length from perturbation theory, and derive the dependence of the Chern number fluctuation on the momentum difference, showing that the saturation results from the short-range correlation.

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions., Comment: To appear in Annual Reviews of Condensed Matter Physics

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model., Comment: v1-->v2: significantly revised, new co-author added; small typo fixed in the most recent version 3

We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time $\bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})}$ for when the system falls out of equilibrium and the associated freeze-out length $\bar{\xi}\sim\tau^{\nu/({1+2\nu z})}$ show power-law scaling with respect to the quench rate $1/\tau$, where the exponents depend on the correlation length exponent $\nu$ and the dynamical exponent $z$ associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

We suggest the tried approach of impurity band engineering to produce flat bands and additional nodes in Dirac materials. We show that surface impurities give rise to nearly flat impurity bands close to the Dirac point. The hybridization of the Dirac nodal state induces the splitting of the surface Dirac nodes and the appearance of new nodes at high-symmetry points of the Brillouin zone. The results are robust and not model dependent: the tight-binding calculations are supported by a low-energy effective model of a topological insulator surface state hybridized with an impurity band. Finally, we address the effects of electron-electron interactions between localized electrons on the impurity site. We confirm that the correlation effects, while producing band hybridization and Kondo effect, keep the hybridized band flat. Our findings open up prospects for impurity band engineering of nodal structures and flat-band correlated phases in doped Dirac materials., Comment: 8 pages, 5 figures

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 66601 (2018)] is applied to nodal line and Weyl semimetals (including graphene), and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drude's inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband scattering. Experiments which can measure these deviations are proposed., Comment: 3 Figures, including supplementary material

Magnetotransport theory of layered superconductors in the flux flow steady state is revisited. Longstanding controversies concerning observed Hall sign reversals are resolved. The conductivity separates into a Bardeen-Stephen vortex core contribution, and a Hall conductivity due to moving vortex charge. This charge, which is responsible for Hall anomaly, diverges logarithmically at weak magnetic field. Its values can be extracted from magetoresistivity data by extrapolation of vortex core Hall angle from the normal phase. Hall anomalies in YBCO, BSCCO, and NCCO data are consistent with theoretical estimates based on doping dependence of London penetration depths. In the appendices, we derive the Streda formula for the hydrodynamical Hall conductivity, and refute previously assumed relevance of Galilean symmetry to Hall anomalies., Comment: Submission to SciPost

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows Markovian dynamics that the entanglement property of the future state can be predicted solely based on the entanglement properties of the current state and the unitary operator at each step. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schr\"odinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits. We perform numerical simulations for these models and demonstrate the validity and prediction power of the entanglement feature approach., Comment: 20 pages, 14 figures

Despite much theoretical effort, there is no complete theory of the 'strange' metal state of the high temperature superconductors, and its linear-in-temperature, $T$, resistivity. Recent experiments showing an unexpected linear-in-field, $B$, magnetoresistivity have deepened the puzzle. We propose a simple model of itinerant electrons, interacting via random couplings with electrons localized on a lattice of quantum 'dots' or 'islands'. This model is solvable in a large-$N$ limit, and can reproduce observed behavior. The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations. For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-$T$ resistivity and a $T \ln T$ specific heat as $T\rightarrow 0$. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-$T$ crossover to a fully incoherent regime that also has a linear-in-$T$ resistivity. We show that the MFL regime has conductivities which scale as a function of $B/T$; however, its magnetoresistance saturates at large $B$. We then consider a macroscopically disordered sample with domains of MFLs with varying densities of electrons. Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field $B$ applied perpendicular to the plane of the sample, at large $B$. The resistance also scales linearly in $T$ at small $B$, and as $T f(B/T)$ at intermediate $B$. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates., Comment: 21 pages + Appendices + References, 4 figures

We show that the topological index of a wavefunction, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, $Z_2$ topological insulators, and Spin-$1$ AKLT and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possible application, we propose a partial quantum tomography scheme from which the topological index of a generic multi-component wavefunction can be extracted by measuring only a small subset of wavefunction components, equivalent to the measurement of a bulk entanglement topological index., Comment: 11 pages including supplementary. v2: Minor text change, reference correction and update. v3: Text and SM update. To appear in Physical Review Letters

Magnetic skyrmions are particle-like objects with topologically-protected stability which can be set into motion with an applied current. Using a particle-based model we simulate current-driven magnetic skyrmions interacting with random quenched disorder and examine the skyrmion velocity fluctuations parallel and perpendicular to the direction of motion as a function of increasing drive. We show that the Magnus force contribution to skyrmion dynamics combined with the random pinning produces an isotropic effective shaking temperature. As a result, the skyrmions form a moving crystal at large drives instead of the moving smectic state observed in systems with a negligible Magnus force where the effective shaking temperature is anisotropic. We demonstrate that spectral analysis of the velocity noise fluctuations can be used to identify dynamical phase transitions and to extract information about the different dynamic phases, and show how the velocity noise fluctuations are correlated with changes in the skyrmion Hall angle, transport features, and skyrmion lattice structure., Comment: 14 pages, 10 figures

For weakly disordered fractional quantum Hall phases, the non linear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wavevectors by electrical transport. Incompressible phases, irradiated at slightly above the magneto-roton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Non linear conductivity can probe composite fermions' charge excitations in compressible filling factors., Comment: 5 Pages, 3 figures. Revised, Added references

Certain non-uniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudo-magnetic field for electrons near the Dirac points. However, this Landau level structure is in general approximate and restricted to low energies. Here we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3 our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d., Comment: 5 + 9 pages; v4: final version including references to hyperdiamond lattices

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical $(2+1)$-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents $z=1.52(3)$, $\nu=1.16(5)$, $\beta/\nu= 0.48(2)$, $\gamma/\nu=2.52(4)$, and $\eta=-0.52(4)$. These values agree with and improve upon earlier Monte-Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments., Comment: 10 pages, 12 figures, final version as published

Recent experiments have reported on controlled nucleation of individual skyrmions in chiral magnets. Here we show that in magnetic ultra-thin films with interfacial Dzyaloshinskii-Moriya interaction, single skyrmions of different radii can be nucleated by creating a local distortion in the magnetic field. In our study, we have considered zero temperature quantum nucleation of a single skyrmion from a ferromagnetic phase. The physical scenario we model is one where a uniform field stabilizes the ferromagnet, and an opposing local magnetic field over a circular spot, generated by the tip of a local probe, drives the skyrmion nucleation. Using spin path integrals and a collective coordinate approximation, the tunneling rate from the ferromagnetic to the single skyrmion state is computed as a function of the tip's magnetic field and the circular spot radius. Suitable parameters for the observation of the quantum nucleation of single skyrmions are identified., Comment: 7 pages, 5 figures

Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs). Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping. In particular, we show how the imaginary gap, which serves as a proxy for band flatness, can be optimized by appealing to Rouche's theorem, a familiar result from complex analysis. This leads to an explicit construction which we illustrate through its application to two-band FCI models with nontrivial topology (i.e. nonzero Chern numbers). We show how the imaginary gap perspective leads to an elegant geometric picture of how topological properties can obstruct band flatness in systems with finite ranged hopping., Comment: 8 pages, 4 figures

We provide a theoretical explanation for the optical modes observed in inelastic neutron scattering (INS) on the bcc solid phase of helium 4 [T. Markovich, E. Polturak, J. Bossy, and E. Farhi, Phys. Rev. Lett. 88, 195301 (2002)]. We argue that these excitations are amplitude (Higgs) modes associated with fluctuations of the crystal order parameter within the unit cell. We present an analysis of the modes based on an effective Ginzburg-Landau model, classify them according to their symmetry properties, and compute their signature in INS experiments. In addition, we calculate the dynamical structure factor by means of an ab intio quantum Monte Carlo simulation and find a finite frequency excitation at zero relative momentum., Comment: 13 pages, 11 figures

We investigate entanglement spectra of the SO(3) bilinear-biquadratic spin-1 chain, a model with phases exhibiting spontaneous symmetry breaking (both translation and spin rotation), points of enlarged symmetry, and a symmetry-protected topological phase (the Haldane phase). Our analysis reveals how these hallmark features are manifested in the entanglement spectra, and highlights the versatility of entanglement spectra as a tool to study one-dimensional quantum systems via small finite size realisations., Comment: 21 pages, 13 figures

We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) [Phys. Rev. Lett. 59, 799 (1987)]. Whereas the AKLT states are created by application of bond singlet operators for SU(2) spins, the simplex solid construction is based on N-simplex singlet operators for SU(N) spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a CP^{N-1} coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of SU(4) edge- and SU(8) face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the SU(3) models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to `order by disorder'., Comment: 16 pages, 19 figures

Two-dimensional topological phases are characterized by TKNN integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using Uhlmann's parallel transport for density matrices (Rep. Math. Phys. 24, 229 (1986)), an integer classification of topological phases can be defined for a finite generalized temperature $T$ or dephasing Lindbladian. This scheme reduces to the familiar TKNN classification for $TT_{{\rm c},2}$, and exhibits a `gapless' intermediate regime where topological indices are not well-defined. We demonstrate these ideas in detail, applying them to Haldane's honeycomb lattice model and the Bernevig-Hughes-Zhang model, and we comment on their generalization to multi-band Chern insulators., Comment: 4 pages, 2 figures, standalone supplemental material. Minor text and reference changes. To appear in Physical Review Letters

We report magnetization, electron spin resonance (ESR), and muon spin relaxation ($\mu $SR) measurements on single crystals of the $S=1/2$ (Cu$% ^{+2}$) kagom\'{e} compound Cu(1,3-benzendicarboxylate). The $\mu $SR is carried to temperatures as low as 45 mK. The spin Hamiltonian parameters are determined from the analysis of the magnetization and ESR data. We find that this compound has anisotropic ferromagnetic interactions. Nevertheless, no spin freezing is observed even at temperatures two orders of magnitude lower than the coupling constants. In light of this finding, the relation between persistent spin dynamics and spin liquid are reexamined., Comment: 5 pages, 4 figures

Weyl Semimetals (WS) are a new class of Dirac-type materials exhibiting a phase with bulk energy nodes and an associated vanishing density of states (DOS). We investigate the stability of this nodal DOS suppression in the presence of local impurities and consider whether or not such a suppression can be lifted by impurity-induced resonances. We find that while a scalar (chemical potential type) impurity can always induce a resonance at arbitrary energy and hence lift the DOS suppression at Dirac/Weyl nodes, for many other impurity types (e.g. magnetic or orbital-mixing), resonances are forbidden in a wide range of energy. We investigate a $4$-band tight-binding model of WS adapted from a physical heterostructure construction due to Burkov, Hook, and Balents, and represent a local impurity potential by a strength $g$ as well as a matrix structure $\Lambda$. A general framework is developed to analyze this resonance dichotomy and make connection with the phase shift picture in scattering theory, as well as to determine the relation between resonance energy and impurity strength $g$. A complete classification of impurities based on $\Lambda$, based on their effect on nodal DOS suppression, is tabulated. We also discuss the differences between continuum and lattice approaches., Comment: 20 pages + appendices, 5 figures. References updated. Figure color changed to improve readability. New section added to discuss the differences between continuum and lattice approaches. Published version

Relativistic O(N) field theories are studied near the quantum critical point in two space dimensions. We compute dynamical correlations by large scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For N=3 and 4 we confirm its \omega^3 rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For N=2, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons, (Josephson arrays) the power law rise above the Higgs mass, increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be \sigma^*_c = 0.3 (\pm 0.1) 4e^2/h. In the appendices, we describe a generalization of the worm algorithm to N>2, and also a singular value decomposition error analysis for the numerical analytic continuation., Comment: 17 pages, 17 figures, revised appendix B, additional references added, corrected typos

Band insulators appear in a crystalline system only when the filling -- the number of electrons per unit cell and spin projection -- is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott insulator, i.e. it is either gapless or, if gapped, displays fractionalized excitations and topological order. We raise the inverse question -- at an integer filling is a band insulator always possible? Here we show that lattice symmetries may forbid a band insulator even at certain integer fillings, if the crystal is non-symmorphic -- a property shared by a majority of three-dimensional crystal structures. In these cases, one may infer the existence of topological order if the ground state is gapped and fully symmetric. This is demonstrated using a non-perturbative flux threading argument, which has immediate applications to quantum spin systems and bosonic insulators in addition to electronic band structures in the absence of spin-orbit interactions., Comment: 5 pages, 3 figures, 1 table in the main text + 4 pages supplementary material. v2 with typos corrected and updated figures and references

We investigate the effects of bulk impurities on the electronic spectrum of Weyl semimetals, a recently identified class of Dirac-type materials. Using a $T$-matrix approach, we study resonant scattering due to a localized impurity in tight binding versions of the continuum models recently discussed by Burkov, Hook, and Balents, describing perturbed four-component Dirac fermions in the vicinity of a critical point. The impurity potential is described by a strength $g$ as well as a matrix structure $\Lambda$. Unlike the case in d-wave superconductors, where a zero energy resonance can always be induced by varying the impurity scalar and/or magnetic impurity strength, we find that for certain types of impurity ($\Lambda$), the Weyl node is protected, and that a scalar impurity will induce an intragap resonance over a wide range of scattering strength. A general framework is developed to address this question, as well as to determine the dependence of resonance energy on the impurity strength., Comment: 5 pages, 4 figures. Minor typo corrected. Published version

We study Haldane's honeycomb lattice model and a bilayer generalization thereof from the perspective of edge states, entanglement spectra, and Wannier function behavior. For the monolayer model, we obtain the zigzag edge states analytically, and identify the edge state crossing point $k_c$ with where the $f = 1/2$ entanglement occupancy and the half-odd-integer Wannier centers occur. A continuous interpolation between the entanglement states and the Wannier states is introduced. We then construct a bilayer model by Bernal stacking two monolayers coupled by interlayer hopping. We analyze a particular limit of this model where an extended symmetry, related to inversion, is present. The band topology then reveals a break-down of the correspondence between edge and entanglement spectrum, which is analyzed in detail, and compared with the inversion-symmetric Z2 topological insulators which show a similar phenomenon., Comment: 24 pages, 10 figures

We examine the quantum entanglement spectra and Wannier functions of the square lattice Hofstadter model. Consistent with previous work on entanglement spectra of topological band structures, we find that the entanglement levels exhibit a spectral flow similar to that of the full system's energy spectrum. While the energy spectra are continuous, with open boundary conditions the entanglement spectra exhibit discontinuities associated with the passage of an energy edge state through the Fermi level. We show how the entanglement spectrum can be understood by examining the band projectors of the full system and their behavior under adiabatic pumping. In so doing we make connections with the original TKNN work on topological two-dimensional band structures and their Chern numbers. Finally we consider Wannier states and their adiabatic flows, and draw connections to the entanglement properties., Comment: 14 + 4 pages, 12 figures. Introductory material expanded. Figures explained in more detail. New appendix added. Minor typographical errors corrected. Published version

The amplitude mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. It is expected in antiferromagnets, short coherence length superconductors, charge density waves, and lattice Bose condensates. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the amplitude mode can decay into low-energy Goldstone modes, its experimental visibility has been questioned. Here we show that the visibility depends on the symmetry of the measured susceptibility. The longitudinal susceptibility diverges at low frequency as \chi_{\sigma\sigma} ~ i/\omega (d=2) or log(1/|\omega|) (d=3), which can completely obscure the amplitude peak. In contrast, the scalar susceptibility is suppressed by four extra powers of frequency, exposing the amplitude peak throughout the ordered phase. We discuss experimental setups for measuring the scalar susceptibility. The conductivity of the O(2) theory (relativistic superfluid) is a scalar response and therefore exhibits suppressed absorption below the Higgs mass threshold, \sigma ~ \omega^{2d+1}. In layered, short coherence length superconductors, (relevant e.g. to cuprates) this threshold is raised by the interlayer plasma frequency., Comment: 17 pages, 9 figures

Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates., Comment: 4.2 pages, 3 figures

Magneto-transport of hard core bosons (HCB) is studied using an XXZ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex hopping energy, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at 6.5x10-5 vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom ('vspin'), which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices, and magnet-transport of short coherence length superconductors., Comment: 15 pages, 15 figures

The quasiparticle interference of the spectroscopic imaging scanning tunneling microscopy has been investigated for the surface states of the large gap topological insulator Bi$_2$Te$_3$ through the T-matrix formalism. Both the scalar potential scattering and the spin-orbit scattering on the warped hexagonal isoenergy contour are considered. While backscatterings are forbidden by time-reversal symmetry, other scatterings are allowed and exhibit strong dependence on the spin configurations of the eigenfunctions at k points over the isoenergy contour. The characteristic scattering wavevectors found in our analysis agree well with recent experiment results., Comment: 5 pages, 2 figures, Some typos are corrected

In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states, and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states (RVB). The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state., Comment: 21 pages, 8 figures, 1 table, minor corrections

We extend the Kitaev model defined for the Pauli-matrices to the Clifford algebra of $\Gamma$-matrices, taking the $4 \times 4$ representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically non-trivial phase carries gapless chiral edge modes along the sample boundary. On the 3D diamond lattice, the ground states can exhibit gapless 3D Dirac cone-like excitations and gapped topological insulating states. Generalizations to even higher rank $\Gamma$-matrices are also discussed., Comment: A revised version

In two dimensions a vortex lattice can melt by quantum fluctuations into a non-superfluid Quantum Vortex Liquid (QVL). To determine the melting conditions, we compute the bare vortex hopping rate by exact diagonalization of square clusters near half filling. Mapping our effective Hamiltonian to the Boson Coloumb Liquid simulated in Phys. Rev. Lett. 73, 826 (1994), we expect a QVL above a melting density of 0.0065 vortices per lattice site. We also compute the Hall conductivity using adiabatic curvatures. As a function of boson filling it reverses sign at half filling in a sharp transition accompanied by a vanishing temperature scale. At half filling, each vortex carries a spin half quantum number (`v-spin'), as a consequence of local non commuting SU(2) symmetries. Implications of these results could be realized in cold atoms, Josephson junction arrays and cuprate superconductors.

These lectures review the large N Schwinger Bosons Mean Field approach to the quantum Heisenberg model. The method applies to ordered and disordered phases in all dimensions, at zero and at finite temperature. Extension to frustrated models is explained. An example for an experimentally useful application, is the temperature dependent staggered magnetization of the layered antiferromagnet., Comment: Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mila

We analyze the electronic properties of a simple stacking defect in Bernal graphite. We show that a bound state forms, which disperses as $|\bfk-\bfK|^3$ in the vicinity of either of the two inequivalent zone corners $\bfK$. In the presence of a strong c-axis magnetic field, this bound state develops a Landau level structure which for low energies behaves as $E\nd_n\propto |n B|^{3/2}$. We show that buried stacking faults have observable consequences for surface spectroscopy, and we discuss the implications for the three-dimensional quantum Hall effect (3DQHE). We also analyze the Landau level structure and chiral surface states of rhombohedral graphite, and show that, when doped, it should exhibit multiple 3DQHE plateaus at modest fields., Comment: 19 pages

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations., Comment: 7 pages, 2 figures

I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT), in which the singlets are extended over N-site simplices. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing us to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, we show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model, with N-spin interactions, on the same lattice. In three and higher dimensions, the SS states can spontaneously break SU(N) and exhibit N-sublattice long-ranged order, as a function of a discrete parameter which fixes the local representation of SU(N). I analyze this transition using a classical mean field approach. For N>2 the ordered state is selected via an "order by disorder" mechanism. As in the AKLT case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary., Comment: 14 pages, 8 figures, minor typos corrected

This paper has been withdrawn and replaced by a new version entitled "Vortex quantum dynamics of two dimensional lattice bosons" By Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas, posted in arXiv:0810.2604. The calculations and results of the original manuscript were correct, and lead to several important conclusions about vortex dynamics and Hall conductance. However, we have dropped our conjecture, that vortices exhibit mutual Fermi statistics. The conjecture was based on the antisymmetry under exchange of two vortices, as revealed in the lowest eight many-body eigenstates of 16 sites toroidal lattices. Appealing to an effective Harper bosons model on larger lattices, revealed vortex eigenstates with both Bose and Fermi permutation symmetries, although vortices do carry spin half quantum numbers. It may exemplify that a general non-relativistic "spin-statistics theorem" in two dimensions does not hold.

We predict the existence of a three dimensional quantum Hall effect plateau in a graphite crystal subject to a magnetic field. The plateau has a Hall conductivity quantized at $\frac{4e^2}{\hbar} \frac{1}{c_0} $ with $c_0$ the c-axis lattice constant. We analyze the three-dimensional Hofstadter problem of a realistic tight-binding Hamiltonian for graphite, find the gaps in the spectrum, and estimate the critical value of the magnetic field above which the Hall plateau appears. When the Fermi level is in the bulk Landau gap, Hall transport occurs through the appearance of chiral surface states. We estimate the magnetic field necessary for the appearance of the three dimensional quantum Hall Effect to be $15.4 $T for electron carriers and $7.0 $T for hole carriers., Comment: Several new references added

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices., Comment: A revised manuscript, including new predictions for observing vortex tunneling effects in cold atoms and superconducting films

We extend the Keldysh formulation to quantum spin systems and derive exact equations of motion. This allows us to explore the dynamics of single spins and of ferromagnets when these are inserted between superconducting leads. Several new effects are reported. Chief amongst these are nutations of single S=1/2 spins in Josephson junctions. These nutations are triggered by the superconducting pairing correlations in the leads. Similarly, we find that on rather universal grounds, magnets display unconventional spin wave dynamics when placed in Josephson junctions. These lead to modifications in the tunneling current., Comment: (14 pages, 5 figures)

We study the effect of the exchange interactions in small superconducting grains near the Coulomb blockade regime. We extend the standard description of the grain in terms of a single collective variable, the charge and its conjugated phase, to include the spin degree of freedom. The suppression of spin fluctuations enhances the tendency towards Coulomb blockade. The effective charging energy and conductance are calculated numerically in the regime of large grain-lead coupling., Comment: 4 pages, 3 figures. Some updates to references, and a new introduction have been included