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arXiv:2208.13767 · Physical review. B./Physical review. B

Transient ballistic sound waves in hot and chaotic fermion lattices

Vir B. Bulchandani, David A. Huse

Published Apr 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Chaotic lattice models at high temperature are generically expected to exhibit diffusive transport of all local conserved charges. Such diffusive transport is usually associated with overdamped relaxation of the associated currents. Here we show that by appropriately tuning the inter-particle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of ``hot band sound''. We study a family of one-dimensional spinless fermion chains with long-range density-density interactions, in which the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed. Our results demonstrate that underdamped sound waves of charge density can arise within a single band, with strong interactions and far from integrability, and at very high temperature.

DOI
10.1103/g821-jc9c

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Chaotic lattice models at high temperature are generically expected to exhibit diffusive transport of all local conserved charges. Such diffusive transport is usually associated with overdamped relaxation of the associated currents. Here we show that by appropriately tuning the inter-particle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of ``hot band sound''. We study a family of one-dimensional spinless fermion chains with long-range density-density interactions, in which the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed. Our results demonstrate that underdamped sound waves of charge density can arise within a single band, with strong interactions and far from integrability, and at very high temperature.
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Integrable and nonintegrable systems have very different transport properties. In this paper, we highlight these differences for specific one-dimensional models of interacting lattice fermions. The technique used is a finite temperature numerical calculation of the adiabatic stiffness (also called the Drude weight or charge stiffness) and isothermal stiffness (also called the ``Meissner'' stiffness) in electrical and energy transport, and the momentum dependent dynamical conductivities $\ensuremath{\sigma}(q,\ensuremath{\omega})$ and $\ensuremath{\kappa}(q,\ensuremath{\omega})$. We apply a flux twist to break the Kramers degeneracy; thus, allowing us to focus on the effect of the dynamical degeneracies in the integrable system. In this situation, we show that the isothermal stiffness goes to zero rapidly with the system size for both types of systems even at high temperatures; while the adiabatic stiffness appears to go to zero in the nonintegrable system and to a finite value in the integrable one. We analyze this difference in terms of the statistics of the current matrix elements and the degeneracies of the systems, and show that in the integrable system, despite the presence of degeneracies, the dominant contribution to the adiabatic stiffness comes from large-current-carrying nondegenerate states. We also show that energy transport at nonzero $\ensuremath{\omega}$ and qqq occurs within a banded continuum in the integrable system indicative of ballistic transport while the nonintegrable system shows diffusion but with the existence of overdamped excitations at large values of momentum.
A variety of recent studies have shed light on the far from equilibrium behavior of quantum systems. Research suggests that this away from equilibrium approach may lead to the realization of unfamiliar dynamical quantum states. For instance, we see ballistic transport at finite temperature, an absence of thermalization, and development of long-range entanglement from initially uncorrelated states. It has been shown that in some cases a time-evolving quantum state is equivalent to the ground state of an "emergent" Hamiltonian where the time enters as a param- eter. This mapping gives us insight into the nature of correlations between particles. For high temperatures, we expect no long-range correlations to develop. However, the emergent model demonstrates that the time-evolved state can be realized as a low energy eigenstate, which naturally possesses long-range correlations. Here, we study the dynamical behavior of both noninteracting and interacting particles in a one-dimensional lattice under various conditions. As the system un- dergoes time evolution, we look at the distribution of particles as well as correlations between particles in the system. We then compare the actual time-evolving state of the system to the ground state of the emergent Hamiltonian to study how long this description is valid. We generally expect that the description is valid in a given region as long as the boundary effects do not propagate into the region. We first verify and reproduce results in the literature (see Vidmar et al. [1]). We proceed to study the effect of interaction strength in a particular interacting model that shows both ballistic and diffusive transport. We then apply this formalism to calculate infinite temperature dynamics of a noninteracting system. Interestingly, this system also develops long-range correlations over time in spite of starting out from an infinite temperature state.
We study transport and relaxation of spinless fermions with long-range Coulomb interactions at high temperatures through numerical simulations of out-of-equilibrium dynamics. We find that the transport and relaxation are continuously slowing down for increasing coupling VVV, and that there is a transition in the type of transport. For intermediate couplings, the system exhibits normal diffusive transport, but the timescale for the onset of that is long. For large couplings, it exhibits subdiffusive transport, while at the same time, the relaxation time diverges exponentially with system lengths, featuring a many-body-localization (MBL)-like phase. We attribute the slow transport to formation of slow bound states and stable clusters of particles. For few-particle systems, we prove the existence, visualize the slowness, and analyze the collision properties of the bound states. For many particles at high densities, there should be a hierarchy of clusters of particles on many different length scales. We argue that at large couplings, the average maximal size of the stable clusters should scale linearly with the length of the lattice, which is in accordance with the MBL-like behavior.
We study sound in Galilean invariant systems of one-dimensional fermions. At low temperatures, we find a broad range of frequencies in which in addition to the waves of density there is a second sound corresponding to the ballistic propagation of heat in the system. The damping of the second sound mode is weak, provided the frequency is large compared to a relaxation rate that is exponentially small at low temperatures. At lower frequencies, the second sound mode is damped, and the propagation of heat is diffusive.
We consider a system of one-dimensional fermions moving in one direction, such as electrons at the edge of a quantum Hall system. At sufficiently long timescales the system is brought to equilibrium by weak interactions between the particles, which conserve their total number, energy, and momentum. The time evolution of the system near equilibrium is described by hydrodynamics based on the three conservation laws. We find that the system supports three sound modes. In the low-temperature limit one mode is a pure oscillation of particle density, analogous to the ordinary sound. The other two modes involve oscillations of both particle and entropy densities. In the presence of disorder, the first sound mode is strongly damped at frequencies below the momentum relaxation rate, whereas the other two modes remain weakly damped.