Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1410.7262 · Physical Review B

Energy and particle currents in a driven integrable system

D. Crivelli, Peter Prelovšek, Marcin Mierzejewski

Published Nov 11, 2014• 4 citations
arXivHTMLPDF

Abstract

We study the ratio of the energy and particle currents (${j}^{E}/{j}^{N}$) in an integrable one-dimensional system of interacting fermions. Both currents are driven by a finite (nonzero) dc electric field. In doped insulators, where the local conserved quantities saturate the so-called Mazur bound on the charge stiffness, ${j}^{E}/{j}^{N}$ agrees with the linear-response theory, even though such agreement may be violated for each current alone. However, in the metallic regime with a nonsaturated Mazur bound, the ratio ${j}^{E}/{j}^{N}$ in a driven system is shown to be much larger than predicted by the linear-response theory.

DOI
10.1103/physrevb.90.195119

Related papers

Nonlinear Current Response of an Isolated System of Interacting Fermions

Marcin Mierzejewski, Peter Prelovšek

Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a nonintegrable case at finite temperatures the major effect of nonlinearity can be taken into account within the linear response formalism extended by a renormalization of the kinetic energy due to the Joule heating. On the other hand, integrable systems show on constant driving a different universality with a damped oscillating current whereby the frequency is related but not equal to the Bloch oscillations.

arXiv:1007.3383•Physical Review Letters•Oct 29, 2010•46 citations

Integrable Mott Insulators Driven by a Finite Electric Field

Marcin Mierzejewski, J. Bonča, Peter Prelovšek

We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of a one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted for by internal heating, the integrability leads to a strongly nonlinear dc response with a vanishingly small dc conductivity in the linear-response regime. The finding is consistent with equilibrium results for the dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.

arXiv:1106.0604•Physical Review Letters•Sep 14, 2011•38 citations

Signatures of diffusion and ballistic transport in the stiffness, dynamical correlation functions, and statistics of one-dimensional systems

Subroto Mukerjee, B. Sriram Shastry

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 $q$ 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.

arXiv:0705.3791•Physical Review B•Jun 24, 2008•39 citations

Evidence for ideal insulating or conducting state in a one-dimensional integrable system

X. Zotos, Peter Prelovšek

Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one-dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low-frequency conductance indicate a fundamental difference between integrable and nonintegrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The nonintegrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9508078•Physical review. B, Condensed matter•Jan 15, 1996•148 citations

Conductivity in a disordered one-dimensional system of interacting fermions

O. S. Barišić, Peter Prelovšek

Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing dc transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the dc conductivity ${\ensuremath{\sigma}}_{0}$ scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase in the effective localization length with the interaction.

arXiv:1009.0211•Physical Review B•Oct 29, 2010•53 citations

Transport and conservation laws

X. Zotos, Félix Naef, Peter Prelovšek

We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.

arXiv:cond-mat/9611007•Physical review. B, Condensed matter•May 1, 1997•533 citations
We study the ratio of the energy and particle currents (jE/jN{j}^{E}/{j}^{N}jE/jN) in an integrable one-dimensional system of interacting fermions. Both currents are driven by a finite (nonzero) dc electric field. In doped insulators, where the local conserved quantities saturate the so-called Mazur bound on the charge stiffness, jE/jN{j}^{E}/{j}^{N}jE/jN agrees with the linear-response theory, even though such agreement may be violated for each current alone. However, in the metallic regime with a nonsaturated Mazur bound, the ratio jE/jN{j}^{E}/{j}^{N}jE/jN in a driven system is shown to be much larger than predicted by the linear-response theory.
Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a nonintegrable case at finite temperatures the major effect of nonlinearity can be taken into account within the linear response formalism extended by a renormalization of the kinetic energy due to the Joule heating. On the other hand, integrable systems show on constant driving a different universality with a damped oscillating current whereby the frequency is related but not equal to the Bloch oscillations.
We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of a one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted for by internal heating, the integrability leads to a strongly nonlinear dc response with a vanishingly small dc conductivity in the linear-response regime. The finding is consistent with equilibrium results for the dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.
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.
Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one-dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low-frequency conductance indicate a fundamental difference between integrable and nonintegrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The nonintegrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime. \textcopyright{} 1996 The American Physical Society.
Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing dc transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the dc conductivity ${\ensuremath{\sigma}}_{0}$ scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase in the effective localization length with the interaction.
We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.