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We study thermal conductivity in one-dimensional electronic fluids combining kinetic [R. Samanta, I. V. Protopopov, A. D. Mirlin, and D. B. Gutman, Thermal transport in one-dimensional electronic fluid, Phys. Rev. Lett. 122, 206801 (2019)] and hydrodynamic [I. V. Protopopov, R. Samanta, A. D. Mirlin, and D. B. Gutman, Anomalous hydrodynamics in one-dimensional electronic fluid, Phys. Rev. Lett. 126, 256801 (2021)] theories. The kinetic approach is developed by partitioning the Hilbert space into bosonic and fermionic sectors. We focus on the regime where the long-living thermal excitations are fermions and compute thermal conductivity. From the kinetic theory standpoint, the fermionic part of thermal conductivity is normal, while the bosonic one is anomalous, that scales as ω–1/3 and thus dominates in the infrared limit. The multi-mode hydrodynamic theory is obtained by projecting the fermionic kinetic equation on the zero modes of its collision integral. On a bare level, both theories agree and the thermal conductivity computed in hydrodynamic theory matches the result of the kinetic equation. The interaction between hydrodynamic modes leads to renormalization and consequently to anomalous scaling of the transport coefficients. In a four-mode regime, all modes are ballistic and the anomaly manifests itself in Kardar-Parisi-Zhang-like broadening with asymmetric power-law tails. "Heads" and "tails" of the pulses contribute equally to thermal conductivity, leading to ω–1/3 scaling of heat conductivity. In the three-mode regime, the system is in the universality class of a classical viscous fluid [Herbert Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014); O. Narayan and S. Ramaswamy, Anomalous heat conduction in one-dimensional momentum-conserving systems, Phys. Rev. Lett. 89, 200601 (2002)]. [ABSTRACT FROM AUTHOR]

Anderson's localization on the edge of a two-dimensional time reversal topological insulator (TI) is studied. For the noninteracting case, the topological protection acts according to the Z2 classification, leading to conducting and insulating phases for odd and even fillings, respectively. In the presence of repulsive interaction, the phase diagram is notably changed. We show that for sufficiently strong values of the interaction, the zero-temperature fixed point of the TI is conducting, including the case of even fillings. We compute the boundaries of the conducting phase for various fillings and types of disorder. [ABSTRACT FROM AUTHOR]

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with nonlinear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature T or weakly interacting bosons at high T. We calculate the equilibration rate which is found to scale with temperature as T5 and T14 in the high-temperature ("bosonic") and the low-temperature ("fermonic") regimes, respectively. The relaxation rate of a hot particle with the momentum k in the fermonic regime scales as k7T7. [ABSTRACT FROM AUTHOR]

We explore the lifetime of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant λ=m*l²T and the bosonic theory by λ-1, where 1/m* and l characterize the curvature of the fermionic and bosonic spectra, respectively, and T is the temperature. [ABSTRACT FROM AUTHOR]

We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a nonlinear single-particle spectrum. We show that, despite the non-Fermi-liquid nature of the problem, nonequilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a nonlinear transformation which decouples the left- and right-moving excitations. Employing this approach, we investigate the kinetics of the phase-space distribution of the quasiparticles and thus determine the time evolution of the density pulse. This allows us to explore a crossover from the essentially free-fermion evolution for weak or short-range interaction to hydrodynamics emerging in the case of sufficiently strong, long-range interaction. [ABSTRACT FROM AUTHOR]

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(l + A B), where A(e) and Bit) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region. [ABSTRACT FROM AUTHOR]

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time, the density profile develops strong oscillations with a period much larger than the Fermi wavelength. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [U(r) ⪢ l/mr² where in is the fermionic mass and r the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation. [ABSTRACT FROM AUTHOR]

It has been shown that solutions of a number of many-body problems out of equilibrium can be expressed in terms of Toeplitz determinants with Fisher-Hartwig (FH) singularities. In the present paper, such Toeplitz determinants are studied numerically. Results of our numerical calculations fully agree with the FH conjecture in an extended form that includes a summation over all FH representations (corresponding to different branches of the logarithms). As specific applications, we consider problems of Fermi edge singularity and tunneling spectroscopy of Luttinger liquid with multiple-step energy distribution functions, including the case of population inversion. In the energy representation, a sum over FH branches produces power-law singularities at multiple edges. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green's functions are calculated under nonequilibrium conditions. The bosonic statistics leads to a Luttinger liquid state with a nonlinear spectrum of collective modes. This results in the suppression of thermal current at low temperatures and affects the single-particle Green's functions. [ABSTRACT FROM AUTHOR]

Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermiedge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of the Toeplitz type. We analyze the long time asymptotics of such determinants, using Szeg&ocedil; and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system. [ABSTRACT FROM AUTHOR]

We study the heat conductivity in Anderson insulators in the presence of a power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal conductivity. For physically relevant cases of two-dimensional and three-dimensional spin systems with 1/r³ dipole-dipole interaction (originating from the conventional 1/r Coulomb interaction between electrons), the found thermal conductivity κ scales with temperature as κ∝T³ and κ∝T4/3, respectively. Our results may be of relevance also to other realizations of random spin Hamiltonians with long-range interactions. [ABSTRACT FROM AUTHOR]

We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities. [ABSTRACT FROM AUTHOR]

Zero-dimensional dissipative action possesses nontrivial minima known as Korshunov instantons. They have been known so far only for imaginary time representation that is limited to equilibrium systems. In this work we reconstruct and generalise Korshunov instantons using real-time Keldysh approach. This allows us to formulate the dissipative action theory for generic nonequilibrium conditions. Possible applications of the theory to transport in strongly biased quantum dots are discussed. [ABSTRACT FROM AUTHOR]

Anderson's localization on the edge of a two-dimensional time reversal topological insulator (TI) is studied. For the noninteracting case, the topological protection acts according to the Z2 classification, leading to conducting and insulating phases for odd and even fillings, respectively. In the presence of repulsive interaction, the phase diagram is notably changed. We show that for sufficiently strong values of the interaction, the zero-temperature fixed point of the TI is conducting, including the case of even fillings. We compute the boundaries of the conducting phase for various fillings and types of disorder. [ABSTRACT FROM AUTHOR]

We discuss two one-dimensional model systems - the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder. [ABSTRACT FROM AUTHOR]

We compare tunneling density of states (TDOS) into two ultrathin Ag films, one uniform and one granular, for different degrees of disorder. The uniform film shows a crossover from Altshuler-Aronov (AA) zero bias anomaly to Efros Shklovskii (ES) like Coulomb gap as the disorder is increased. The granular film, on the other hand, exhibits AA behavior even deeply in the insulating regime. We analyze the data and find that granularity introduces a new regime for the TDOS. While the conductivity is dominated by hopping between clusters of grains and is thus insulating, the TDOS probes the properties of an individual cluster which is "metallic." [ABSTRACT FROM AUTHOR]

We study wave propagation in interacting Bose liquid, where the short-range part of the interaction between atoms is of a hard-core type, and its long-range part scales with a distance as a power law. The cases of Coulomb, dipole-dipole and van der Waals interaction are considered. We employ a hydrodynamic approach, based on the exact solution of the Lieb-Liniger model, and study the evolution of a density pulse instantly released from a potential trap. We analyze semiclassical Euler and continuity equations and construct the corresponding Riemann invariants. We supplement our analysis with numerical calculations and discuss experimental applications for ultracold atom experiments. [ABSTRACT FROM AUTHOR]

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω-1/3scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002)., H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω-1/3scaling of heat conductivity. [ABSTRACT FROM AUTHOR]

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω-1/3 and L1/3, of heat conductivity with the frequency ω and system size L, respectively. [ABSTRACT FROM AUTHOR]

We study the effect of inelastic processes on the magnetotransport of a quasi-one-dimensional Weyl semimetal, using a modified Boltzmann-Langevin approach. The magnetic field drives a crossover to a ballistic regime in which the propagation along the wire is dominated by the chiral anomaly, and the role of fluctuations inside the sample is exponentially suppressed. We show that inelastic collisions modify the parametric dependence of the current fluctuations on the magnetic field. By measuring shot noise as a function of a magnetic field, for different applied voltage, one can estimate the electron-electron inelastic length lee. [ABSTRACT FROM AUTHOR]