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Two-dimensional topological phases are characterized by Thouless-Kohmoto-Nightingale-den Nijs 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 Thouless-Kohmoto-Nightingale-den Nijs classification for T < T c,1 becomes trivial for T > Tc,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 multiband Chem insulators. [ABSTRACT FROM AUTHOR]

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 cylindrical 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 work by Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) [Phys. Rev. Lett. 49, 405 (1982)] 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. [ABSTRACT FROM AUTHOR]

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 066601 (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 currents. Experiments which can measure these deviations are proposed. [ABSTRACT FROM AUTHOR]

For weakly disordered fractional quantum Hall phases, the nonlinear 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 wave vectors by electrical transport. Incompressible phases, irradiated at slightly above the magnetoroton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Nonlinear conductivity can probe composite fermions' charge excitations in compressible filling factors. [ABSTRACT FROM AUTHOR]

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 Rouché'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-range hopping. [ABSTRACT FROM AUTHOR]

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium 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 superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates. [ABSTRACT FROM AUTHOR]

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 lm χσ σ ~ ω-1 (d = 2) or log(1/|w|) (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 0(2) theory (relativistic superfluid) is a scalar response and therefore exhibits suppressed absorption below the Higgs mass threshold, σ ~ ω2d+1. In layered, short coherence length superconductors, (relevant, e.g., to cuprates) this threshold is raised by the interlayer plasma frequency. [ABSTRACT FROM AUTHOR]

We show that the topological index of a wave function, 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, Z2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki 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 multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index. [ABSTRACT FROM AUTHOR]

Magnetic skyrmions are particlelike 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. [ABSTRACT FROM AUTHOR]

Certain nonuniform 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 pseudomagnetic 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. [ABSTRACT FROM AUTHOR]

We report magnetization, electron-spin resonance (ESR), and muon-spin relaxation (μSR) measurements on single crystals of the S = 1/2 (Cu+2) kagome compound Cu(1,3-benzendicarboxylate). The μSR 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 liquids on kagome lattices is reexamined. [ABSTRACT FROM AUTHOR]

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 ω3 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 σc" = 0.3(±0.1) × 4e2/h and describe a generalization of the worm algorithm to N > 2. We use a singular value decomposition error analysis for the numerical analytic continuation [ABSTRACT FROM AUTHOR]

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 Phys. Rev. B 84 235126 (2011)], 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 Λ. Unlike the case in d-wave superconductors, where a zero energy resonance can always be induced by varying the scalar and/or magnetic impurity strength, we find that for certain types of impurity (Λ), 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. [ABSTRACT FROM AUTHOR]

We provide a theoretical explanation for the optical modes observed in inelastic neutron scattering on the bcc solid phase of helium 4 [T. Markovich et al., 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 inelastic neutron scattering 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. [ABSTRACT FROM AUTHOR]

We show that the topological index of a wave function, 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&#95;{2} topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki 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 multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.

Two-dimensional topological phases are characterized by Thouless-Kohmoto-Nightingale-den Nijs 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).

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium 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 superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

We study hard-core lattice bosons in a magnetic field near half filling. The bare vortex hopping rate is extracted from exact diagonalizations of square clusters. We deduce a quantum melting of the vortex lattice above vortex density of 6.5x10(-3) per lattice site. The Hall conductivity reverses sign abruptly as the density crosses half filling, where its characteristic temperature scale vanishes. We prove that at precisely half filling, each vortex carries a spin-1/2 quantum number ("v spin"). Experimental implications of these results are discussed.

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 4e2/variant Planck's over 2pi 1/c0 with c0 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 effect to be 15.4 T for electron carriers and 7.0 T for holes.