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We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of 'boundary MBL' and 'boundary baths'). [ABSTRACT FROM AUTHOR]

We study three-dimensional systems where the parent metallic state contains a loop of Weyl points. We introduce the minimal k • p Hamiltonian, and discuss its symmetries. Guided by this symmetry analysis, we classify the superconducting instabilities that may arise. For a doped Weyl loop material, we argue that-- independent of microscopic details--the leading superconducting instability should be to a fully gapped chiral superconductor in three dimensions--an unusual state made possible only by the nontrivial topology of the Fermi surface. This state, which we dub the "meron superconductor," is neither fully topological nor fully trivial. Meanwhile, at perfect compensation additional states are possible (including some that are fully topological), but the leading instability depends on microscopic details. We discuss the influence of disorder on pairing. In the presence of a spin degeneracy ("Dirac loops") still more complex superconducting states can arise, including a "skyrmion" superconductor with topological properties similar to superfluid He III-B, which additionally breaks lattice rotation symmetry and exhibits nematic order. [ABSTRACT FROM AUTHOR]

We examine what happens when a strongly many-body localized system is coupled to a weak heat bath, with both system and bath containing similar numbers of degrees of freedom. Previous investigations of localized systems coupled to baths operated in regimes where the back action of the system on the bath is negligible and concluded that the bath generically thermalizes the system. In this paper we show that when the system is strongly localized and the bath is only weakly ergodic, the system can instead localize the bath. We demonstrate this both in the limit of weak coupling between system and bath and in the limit of strong coupling and also for two different types of "weak" bath--baths which are close to an atomic limit and baths which are close to a noninteracting limit. The existence of this "many-body localization proximity effect" indicates that many-body localization is more robust than previously appreciated, and it can not only survive coupling to a (weak) heat bath but can even destroy the bath. [ABSTRACT FROM AUTHOR]

We examine the response of a system localized by disorder to a time-dependent local perturbation that varies smoothly with a characteristic timescale τ. We find that such a perturbation induces a nonlocal response, involving a rearrangement of conserved quantities over a length scale ∼ln τ. This effect lies beyond linear response, is absent in undisordered insulators and highlights the remarkable subtlety of localized phases. The effect is common to both single-particle and many-body localized phases. Our results have implications for numerous fields, including topological quantum computation in quantum Hall systems, quantum control in disordered environments, and time-dependent localized systems. For example, they indicate that attempts to braid quasiparticles in quantum Hall systems or Majorana nanowires will not succeed if the manipulations are performed asymptotically slowly, and thus using such platforms for topological quantum computation will require considerable engineering. They also establish that disorder-localized insulators suffer from a statistical orthogonality catastrophe. [ABSTRACT FROM AUTHOR]

We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that widely used diagnostics (such as many-body level statistics and expectation values in exact eigenstates) cease to show signatures of many-body localization above a critical coupling that is exponentially small in the size of the environment. However, we also identify alternative diagnostics for many-body localization, in the spectral functions of local operators. Diagnostics include a discrete spectrum and a hierarchy of energy gaps, including a universal gap at zerofrequency. These alternative diagnostics are shown to be robust, and continue to show signatures of many-body localization as long as the coupling to the bath is weaker than the characteristic energy scales in the system. We also examine how these signatures disappear when the coupling to the environment becomes larger than the characteristic energy scales of the system. [ABSTRACT FROM AUTHOR]

We develop a mean-field theory of the metallic phase near the many-body localization (MBL) transition, using the observation that a system near the MBL transition should become an increasingly slow heat bath for its constituent parts. As a first step, we consider the properties of a many-body localized system coupled to a generic ergodic bath whose characteristic dynamical time scales are much slower than those of the system. As we discuss, a wide range of experimentally relevant systems fall into this class; we argue that relaxation in these systems is dominated by collective many-particle rearrangements, and compute the associated time scales and spectral broadening. We then use the observation that the self-consistent environment of any region in a nearly localized metal can itself be modeled as a slowly fluctuating bath to outline a self-consistent mean-field description of the nearly localized metal and the localization transition. In the nearly localized regime, the spectra of local operators are highly inhomogeneous and the typical local spectral linewidth is narrow. The local spectral linewidth is proportional to the dc conductivity, which is small in the nearly localized regime. This typical linewidth and the dc conductivity go to zero as the localized phase is approached, with a scaling that we calculate, and which appears to be in good agreement with recent experimental results. [ABSTRACT FROM AUTHOR]

We consider d-dimensional systems which are localized in the absence of interactions, but whose single-particle localization length diverges near a discrete set of (single-particle) energies, with critical exponent v. This class includes disordered systems with intrinsic or symmetry protected topological bands, such as disordered integer quantum Hall insulators. We show that such marginally localized systems exhibit anomalous properties intermediate between localized and extended, including vanishing dc conductivity but subdiffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short-range interactions trigger delocalization for partially filled bands at nonzero energy density if v ⩾ 1 /d. We use the Harris-Chayes bound v ⩾ 2/d to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at nonzero energy density. [ABSTRACT FROM AUTHOR]

We discuss whether localization in the two-dimensional continuum can be stable in the presence of short-range interactions. We conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature T < Tc, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized and perhaps even truly many-body localized, depending on how certain rare regions behave. Meanwhile, for T > Tc, perturbation theory fails to converge, which we interpret as interaction-mediated delocalization. We calculate the boundary of the region of perturbative stability of localization in the interaction-strength-temperature plane. We also discuss the behavior in a speckle disorder(relevant for cold-atom experiments) and conclude that perturbation theory about the noninteracting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many-body localization in the two-dimensional continuum cannot survive away from the impurity limit. [ABSTRACT FROM AUTHOR]

We consider fully many-body-localized systems, i.e., isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators. These localized operators are interacting pseudospins, and the Hamiltonian is such that unitary time evolution produces dephasing but not "flips" of these pseudospins. As a result, an initial quantum state of a pseudospin can in principle be recovered via (pseudospin) echo procedures. We discuss how the exponentially decaying interactions between pseudospins lead to logarithmic-in-time spreading of entanglement starting from nonentangled initial states. These systems exhibit multiple different length scales that can be defined from exponential functions of distance; we suggest that some of these decay lengths diverge at the phase transition out of the fully many-body-localized phase while others remain finite. [ABSTRACT FROM AUTHOR]

We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. These spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a "soft gap" at zero frequency in the spatially averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and we find that some characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. We discuss the crossover to localization that occurs as the coupling to the external bath is tuned to zero. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for experiments on many-body localization. [ABSTRACT FROM AUTHOR]

We construct a low-energy effective field theory of fermions interacting via short-range interactions in a simple two-band model of a Weyl semimetal on the cubic lattice and investigate possible broken-symmetry ground states through a one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Hamiltonian to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to explore possible broken-symmetry ground states, we calculate susceptibilities in the particle-hole and particle-particle channels along this trajectory and find that the leading instability is towards a fully gapped spin-density wave (SDW) ground state. The sliding mode of this SDW couples to the external electromagnetic fields in the same way as the Peccei-Quinn axion field of particle physics. We also study the maximally symmetric version of our model with a single independent coupling constant. Possible ground states in this case are either gapless ferromagnetic states where the spin waves couple to the Weyl fermions like the spatial components of a (possibly chiral) gauge field, or a fully gapped spin-singlet Fulde Ferrell-Larkin-Ovchinnikov superconducting state. [ABSTRACT FROM AUTHOR]

We analyze the pairing instabilities for fermions on hexagonal lattices (both honeycomb and triangular ones) in a wide range of fermionic densities ranging from van Hove density at which a single large Fermi surface splits into two disconnected Fermi pockets, to a density at which disconnected pockets shrink to Fermi points (half-filling for a honeycomb lattice and full filling for a triangular lattice). We argue that for a generic doping in this range, superconductivity at weak coupling is of Kohn-Luttinger type, and, due to the presence of electronic interactions beyond on-site repulsion, is a threshold phenomenon, with superconductivity emerging only if the attraction generated by the Kohn-Luttinger mechanism exceeds the bare repulsion in some channel. For disconnected Fermi pockets, we predict that Kohn-Luttinger superconductivity, if it occurs, is likely to be f wave. While the Kohn-Luttinger analysis is adequate over most of the doping range, a more sophisticated analysis is needed near van Hove doping. We treat van Hove doping using a parquet renormalization group, the equations for which we derive and analyze. Near this doping level, superconductivity is a universal phenomenon, arising from any choice of bare repulsive interactions. The strongest pairing instability is into a chiral d-wave state (d + id). At a truly weak coupling, the strongest competitor is a spin-density-wave instability, however, d-wave superconductivity still wins. Moreover, the feedback of the spin density fluctuations into the Cooper channel significantly enhances the critical temperature over the estimates of the Kohn-Luttinger theory. We analyze renormalization group equations at stronger couplings and find that the main competitor to rf-wave superconductivity away from weak coupling is actually ferromagnetism. We also discuss the effect of the edge fermions and show that they are unimportant in the asymptotic weak coupling limit, but may give rise to, e.g., a charge-density-wave order at moderate coupling strengths. [ABSTRACT FROM AUTHOR]

Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate, even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order, in that individual many-body eigenstates can break symmetries or display topological order in the infinite-volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e., localization protects order. In addition, localized systems can move between ordered and disordered localized phases via nonthermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a "spectral transition" involving a sharp change in the spectral statistics of the many-body Hamiltonian. [ABSTRACT FROM AUTHOR]

We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N. For N = 7 the bands become nearly flat, with a small bandwidth ∼3.6 meV. The two nearly flat bands coming from the K and K' valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the band crossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the local Berry curvature of the bands endows the system with a nontrivial quantum geometry. The quantum geometry effects manifest themselves through the quantum distance (Fubini-Study) metric, rather than the more conventional Chem number. Multilayer graphene on BN thus provides a platform for investigating the effect of interactions in a system with a nontrivial quantum distance metric, without the complication of nonzero Chern numbers. We note in passing that flat bands with nonzero Chern number can also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry. [ABSTRACT FROM AUTHOR]

We show that the probability of electric-field-induced interband tunneling in solid-state systems is generically a nonmonotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low-energy dispersion relation contains higher order terms in addition to the usual p2 term. Such higher order terms are generically present, albeit with small coefficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first "Zener oscillation" occurs at a transmission probability which is exponentially small when the coefficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of p in the low-energy dispersion relation. Since odd powers of p are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the p4 term makes the leading contribution. [ABSTRACT FROM AUTHOR]

We study the effect of disorder on massless, spinful Dirac fermions in two spatial dimensions with attractive interactions, and show that the combination of disorder and attractive interactions is deadly to the Dirac semimetal phase. First, we derive the zero temperature phase diagram of a clean Dirac fermion system with tunable doping level (μ) and attraction strength (g). We show that it contains two phases: a superconductor and a Dirac semimetal. Then we add disorder and show that arbitrarily weak disorder destroys the Dirac semimetal, turning it into a superconductor instead. Thus for Dirac fermions near charge neutrality, disorder actually assists superconductivity. We discuss the strength of the superconductivity for both long range and short range disorder. For long range disorder, the superconductivity is exponentially weak in the disorder strength. For short range disorder, a uniform mean field analysis predicts that superconductivity should be doubly exponentially weak in the disorder strength. However, a more careful treatment of mesoscopic fluctuations suggests that locally superconducting puddles should form at a much higher temperature, and should establish global phase coherence at a temperature that is only exponentially small in weak disorder. Thus, mesoscopic fluctuations exponentially enhance the superconducting critical temperature. We also discuss the effect of disorder on the quantum critical point of the clean system, building in the effect of disorder through a replica field theory. We show that disorder is a relevant perturbation to the supersymmetric quantum critical point. We expect that in the presence of attractive interactions, the flow away from the critical point ends up in the superconducting phase, although firm conclusions cannot be drawn since the renormalization group analysis flows to strong coupling. We argue that although we expect the quantum critical point to get buried under a superconducting phase, signatures of the critical point may be visible in the finite temperature quantum critical regime. Our results have implications for experiments on proximity induced superconductivity in Dirac fermion systems, where they imply an enormous disorder enhancement of the superconducting susceptibility. As a result, the proximity induced superconductivity in dirty systems is expected to be much stronger than that in clean systems at the Dirac point. [ABSTRACT FROM AUTHOR]

We study the interplay between superconductivity and spin-density-wave order in graphene doped to 3/8 or 5/8 filling (a van Hove doping). At this doping level, the system is known to exhibit weak-coupling instabilities to both chiral d + id superconductivity and to a uniaxial spin density wave. Right at van Hove doping, the superconducting instability is strongest and emerges at the highest Tc, but slightly away from van Hove doping, a spin density wave likely emerges first. We investigate whether at some lower temperature superconductivity and spin density waves coexist. We derive the Landau-Ginzburg functional describing interplay of the two order parameters. Our calculations show that superconductivity and spin-density-wave order do not coexist and are separated by first-order transitions, either as a function of doping or as a function of T. [ABSTRACT FROM AUTHOR]

We present a fractionalized metallic phase which is indistinguishable from the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in one-electron properties, such as the electron spectral function. We dub this phase the "orthogonal metal." The orthogonal metal and the transition to it from the Fermi liquid are naturally described using a slave-particle representation wherein the electron is expressed as a product of a fermion and a slave Ising spin. We emphasize that when the slave spins are disordered, the result is not a Mott insulator (as erroneously assumed in the prior literature), but rather the orthogonal metal. We construct prototypical ground-state wave functions for the orthogonal metal by modifying the Jastrow factor of Slater-Jastrow wave functions that describe ordinary Fermi liquids. We further demonstrate that the transition from the Fermi liquid to the orthogonal metal can, in some circumstances, provide a simple example of a continuous destruction of a Fermi surface with a critical Fermi surface appearing right at the critical point. We present exactly soluble models that realize an orthogonal metal phase, and the phase transition to the Fermi liquid. These models thus provide valuable solvable examples for phase transitions associated with the death of a Fermi surface. [ABSTRACT FROM AUTHOR]

We point out that a system which supports chiral superconductivity should also support a chiral pseudogap phase: a finite temperature phase wherein superconductivity is lost but time-reversal symmetry is still broken. This chiral pseudogap phase can be viewed as a state with phase incoherent Cooper pairs of a definite angular momentum. This physical picture suggests that the chiral pseudogap phase should have definite magnetization, should exhibit a (nonquantized) charge Hall effect, and should possess protected edge states that lead to a quantized thermal Hall response. We explain how these phenomena are realized in a Ginzburg-Landau description, and comment on the experimental signatures of the chiral pseudogap phase. We expect this work to be relevant for all systems that exhibit chiral superconductivity, including doped graphene and strontium ruthenate. [ABSTRACT FROM AUTHOR]

We consider electrons on a honeycomb or triangular lattice doped to the saddle point of the band structure. We assume the system parameters are such that spin density wave (SDW) order emerges below a temperature TN and investigate the nature of the SDW phase. We argue that at T < TN, the system develops a uniaxial SDW phase whose ordering pattern breaks 0(3) X Z4 symmetry and corresponds to an eight-site unit cell with nonuniform spin moments on different sites. This state is a half-metal-it preserves the full original Fermi surface, but has gapless charged excitations in one spin branch only. It allows for electrical control of spin currents and is desirable for nanoscience. [ABSTRACT FROM AUTHOR]

Chiral superconductivity, which breaks time-reversal symmetry, can exhibit a wealth of fascinating properties that are highly sought after for nanoscience applications. We identify doped graphene monolayer as a system where chiral superconductivity can be realized. In this material, a unique situation arises at a doping where the Fermi surface is nested and the density of states is singular. In this regime, d-wave superconductivity can emerge from repulsive electron-electron interactions. Using a renormalization group method, we argue that superconductivity dominates over all competing orders for generic weak repulsive interactions. Superconductivity develops simultaneously in two degenerate d-wave pairing channels. We argue that the resulting superconducting state is of chiral type, with the phase of the superconducting order parameter winding by 4? around the Fermi surface. Realization of this state in doped graphene will prove that superconductivity can emerge from electron-electron repulsion, and will open the door to applications of chiral superconductivity. [ABSTRACT FROM AUTHOR]

The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero interband matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time-reversal symmetry and lattice rotation symmetry, respec- tively. These optical signatures, which undergo a resonant enhancement in the near-infrared regime, lie well within reach of existing experimental techniques. [ABSTRACT FROM AUTHOR]

Inspired by recent experiments on many-body localized systems coupled to an environment, we apply a Flow Equation method to study the problem of a disorder chain of spinless fermions, coupled via density-density interactions to a second clean chain of spinless fermions. In particular, we focus on the conditions for the onset of a many-body localized phase in the clean sector of our model by proximity to the dirty one. We find that a many-body localization proximity effect in the clean component is established when the density of dirty fermions exceeds a threshold value. From the flow equation method we find that, similar to many-body localization in a single chain, the many-body localization proximity effect is also described by an extensive set of local integrals of motion. Furthermore, by tuning the geometry of the inter-chain couplings, we show that the dynamics of the model is ruled, on intermediate time scales, by an emergent set of quasi-conserved charges. [ABSTRACT FROM AUTHOR]

In nodal-line semimetals, Coulomb interactions and short-range correlated disorder are both marginal perturbations to the clean noninteracting Hamiltonian. We analyze their interplay using a weak-coupling renormalization group approach. In the clean case, the Coulomb interaction has been found to be marginally irrelevant, leading to Fermi liquid behavior. We extend the analysis to incorporate the effects of disorder. The nodal line structure gives rise to kinematical constraints similar to that for a two-dimensional Fermi surface, which plays a crucial role in the one-loop renormalization of the disorder couplings. For a twofold degenerate nodal loop (Weyl loop), we show that disorder flows to strong coupling along a unique fixed trajectory in the space of symmetry inequivalent disorder couplings. Along this fixed trajectory, all symmetry inequivalent disorder strengths become equal. For a fourfold degenerate nodal loop (Dirac loop), disorder also flows to strong coupling, however, the strengths of symmetry inequivalent disorder couplings remain different. We show that feedback from disorder reverses the sign of the beta function for the Coulomb interaction, causing the Coulomb interaction to flow to strong coupling as well. However, the Coulomb interaction flows to strong coupling asymptotically more slowly than disorder. Extrapolating our results to strong coupling, we conjecture that at low energies nodal line semimetals should be described by a noninteracting nonlinear sigma model. We discuss the relation of our results with possible many-body localization at zero temperatures in such materials. [ABSTRACT FROM AUTHOR]

We study surface superconductivity involving the "drumhead" surface states of (doped) Weyl loop materials. The leading weak-coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with p+ip symmetry. We show that the surface SC state is "topological" as long as it is fully gapped, and the system traps Majorana modes wherever a vortex line enters or exits the bulk. In contrast to true two-dimensional p+ip superconductors, these Majorana zero modes arise even in the "strong pairing" regime where the chemical potential is entirely above/below the drumhead. We also consider conventional s-wave pairing, and show that in this case the surface hosts a flat band of charge neutral Majorana fermions, whose momentum range is given by the projection of the bulk Fermi surface. Weyl loop materials thus provide access to new forms of topological superconductivity. [ABSTRACT FROM AUTHOR]

We study the entanglement spectrum in the many-body localizing and thermalizing phases of one- and two-dimensional Hamiltonian systems and periodically driven "Floquet" systems. We focus on the level statistics of the entanglement spectrum as obtained through numerical diagonalization, finding structure beyond that revealed by more limited measures such as entanglement entropy. In the thermalizing phase the entanglement spectrum obeys level statistics governed by an appropriate random matrix ensemble. For Hamiltonian systems this can be viewed as evidence in favor of a strong version of the eigenstate thermalization hypothesis (ETH). Similar results are also obtained for Floquet systems, where they constitute a result "beyond ETH" and show that the corrections to ETH governing the Floquet entanglement spectrum have statistical properties governed by a random matrix ensemble. The particular random matrix ensemble governing the Floquet entanglement spectrum depends on the symmetries of the Floquet drive and therefore can depend on the choice of origin of time. In the many-body localized phase the entanglement spectrum is also found to show level repulsion, following a semi-Poisson distribution (in contrast to the energy spectrum, which follows a Poisson distribution). This semi-Poisson distribution is found to come mainly from states at high entanglement energies. The observed level repulsion occurs only for interacting localized phases. We also demonstrate that equivalent results can be obtained by calculating with a single typical eigenstate or by averaging over a microcanonical energy window, a surprising result in the localized phase. This discovery of new structure in the pattern of entanglement of localized and thermalizing phases may open up new lines of attack on many-body localization, thermalization, and the localization transition. [ABSTRACT FROM AUTHOR]

We investigate the role of symmetries in determining the random matrix class describing quantum thermalization in a periodically driven many-body quantum system. Using a combination of analytical arguments and numerical exact diagonalization, we establish that a periodically driven "Floquet" system can be in a different random matrix class from the instantaneous Hamiltonian. A periodically driven system can thermalize even when the instantaneous Hamiltonian is integrable. A Floquet system that thermalizes in general can display integrable behavior at commensurate driving frequencies. When the instantaneous Hamiltonian and the Floquet operator both thermalize, the Floquet problem can be in the unitary class while the instantaneous Hamiltonian is always in the orthogonal class, and vice versa. We extract general principles regarding when a Floquet problem can thermalize to a different symmetry class from the instantaneous Hamiltonian. A (finite-sized) Floquet system can even display crossovers between different random matrix classes as a function of driving frequency. [ABSTRACT FROM AUTHOR]

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a nonmonotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to "borrow" energy from the bath. But, above a certain coupling the bath produces localization because of an orthogonality catastrophe, whereby the bath "dresses" the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno localization" since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization. [ABSTRACT FROM AUTHOR]

We study three-dimensional (3D) Dirac fermions with weak finite-range scalar potential disorder. In the clean system, the density of states vanishes quadratically at the Dirac point. Disorder is known to be perturbatively irrelevant, and previous theoretical work has assumed that the Dirac semimetal phase, characterized by a vanishing density of states, survives at weak disorder, with a finite disorder phase transition to a diffusive metal with a nonvanishing density of states. In this paper, we show that nonperturbative effects from rare regions, which are missed by conventional disorder-averaged calculations, instead give rise to a nonzero density of states for any nonzero disorder. Thus, there is no Dirac semimetal phase at nonzero disorder. The results are established both by a heuristic scaling argument and via a systematic saddle-point analysis. We also discuss transport near the Dirac point. At the Dirac point, we argue that transport is diffusive, and proceeds via hopping between rare resonances. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the dc conductivity. We derive a scaling theory of transport near disordered 3D Dirac points. We also discuss the interplay of disorder with attractive interactions at the Dirac point and the resulting granular superconducting and Bose glass phases. Our results are relevant for all 3D systems with Dirac points, including Weyl semimetals. [ABSTRACT FROM AUTHOR]

We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in x and y directions, and C4 lattice rotation symmetry. The Kerr angle θK in C4-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity σxy - σyx. We show that this result holds when C4 symmetry is broken. We show that in order for σxy and σyx to be nonzero the mirror symmetries in x and y directions have to be broken, and that for σxy - σyx to be nonzero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a nonzero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a nonzero θK in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from (π,π) and has to include particle-hole asymmetry. Alternatively, in the presence of disorder, one can get a nonzero θK from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. The impurity analysis in our case is similar to that in earlier works on Kerr effect in px + ipy superconductors, however, in our case, the magnitude of θK is enhanced by the flattening of the Fermi surface in the "hot" regions, which mostly contribute to charge order. [ABSTRACT FROM AUTHOR]

We numerically study the interplay between superconductivity and disorder on the graphene honeycomb lattice with on-site Hubbard attractive interactions U using a spatially inhomogeneous self-consistent Bogoliubov-de Gennes (BdG) approach. In the absence of disorder there are two phases at charge neutrality. Below a critical value Uc for attractive interactions there is a Dirac semimetal phase and above it there is a superconducting phase. We add scalar potential disorder to the system, while remaining at charge neutrality on average. Numerical solution of the BdG equations suggests that while in the strong attraction regime (U > Uc) disorder has the usual effect of suppressing superconductivity, in the weak attraction regime (U < Uc) weak disorder enhances superconductivity. In the weak attraction regime, disorder that is too strong eventually suppresses superconductivity, i.e., there is an optimal disorder strength that maximizes the critical temperature Tc. Our numerical results also suggest that in the weakly disordered regime, mesoscopic inhomogeneities enhance superconductivity significantly more than what is predicted by a spatially uniform mean-field theory in the manner of Abrikosov and Gorkov. In this regime, superconductivity consists of rare phase-coherent superconducting islands. We also study the enhancement of the superconducting proximity effect by disorder and mesoscopic inhomogeneities, and obtain typical spatial plots of the tunneling density of states and the superfluid susceptibility that can be directly compared to scanning tunneling microscopy experiments on proximity-induced superconductivity in graphene. [ABSTRACT FROM AUTHOR]

We show that the spin-density wave state on the partially filled honeycomb and triangular lattices is preempted by a paramagnetic phase that breaks an emergent Z4 symmetry of the system associated with the four inequivalent arrangements of spins in the quadrupled unit cell. Unlike other emergent paramagnetic phases in itinerant and localized-spin systems, this state preserves the C6 rotational symmetry of the lattice, but breaks its translational symmetry, giving rise to a superlattice structure that can be detected by scanning tunneling microscopy. This emergent phase also has distinctive signatures in the magnetic spectrum that can be probed experimentally. [ABSTRACT FROM AUTHOR]