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

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Alberto Biella, Mario Collura, Davide Rossini, Andrea De Luca, Leonardo Mazza

Published Jan 1, 2019• 20 citations
OpenAlex

Abstract

Abstract Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

Related papers

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Alberto Biella, Mario Collura, Davide Rossini +2 more

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

arXiv:1905.00088•Nature Communications•Oct 23, 2019•29 citations

Quantum transport of strongly interacting fermions in one dimension far out of equilibrium

Jie Zou, Xiaopeng Li

In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.

arXiv:2206.13023•Physical Review A•Nov 28, 2022•1 citation

A nonequilibrium quantum phase transition in strongly coupled spin chains

Eduardo Mascarenhas, Giacomo Giudice, Vincenzo Savona

We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.

arXiv:1703.02934•Quantum•Dec 20, 2017•11 citations

Ballistic front dynamics after joining two semi-infinite quantum Ising chains

Gabriele Perfetto, Andrea Gambassi

We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasiparticles which characterize the ensuing unitary dynamics. Within the so-called semiclassical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasiparticles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.

arXiv:1704.03437•Physical review. E•Jul 19, 2017•71 citations

Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

Shinya Ae

Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.

arXiv:2605.01645•May 2, 2026•0 citations

Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain

Adam J. McRoberts, Roderich Moessner

Motivated by recent experiments on Google’s sycamore NISQ platform on the spin transport resulting from a non-unitary periodic boundary drive of an XXZ chain, we study a classical variant thereof by a combination of analytical and numerical means. We find the classical model reproduces the quantum results in remarkable detail, and provides an analytical handle on the nature and shape of the spin transport’s three distinct regimes: ballistic (easy-plane), subdiffusive (isotropic) and insulating (easy-axis). Further, we show that this phenomenology is remarkably robust to the inclusion of bond disorder – albeit that the transient dynamics approaching the steady states differs qualitatively between the clean and disordered cases – providing an accessible instance of ballistic transport in a disordered setting.

arXiv:2407.13816•SciPost Physics•Jan 14, 2025•2 citations
Abstract Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.
Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.
In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.
We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.
We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasiparticles which characterize the ensuing unitary dynamics. Within the so-called semiclassical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasiparticles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.
Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length NNN, the equal-time two-point spin correlation function is scaled up to O(1/N)O(1/N)O(1/N). In the state where the ballistic spin transport decays at high temperature TTT, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to 1/T1/T1/T in the limit T→∞T\to\inftyT→∞ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the 1/N1/N1/N-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.
Motivated by recent experiments on Google’s sycamore NISQ platform on the spin transport resulting from a non-unitary periodic boundary drive of an XXZ chain, we study a classical variant thereof by a combination of analytical and numerical means. We find the classical model reproduces the quantum results in remarkable detail, and provides an analytical handle on the nature and shape of the spin transport’s three distinct regimes: ballistic (easy-plane), subdiffusive (isotropic) and insulating (easy-axis). Further, we show that this phenomenology is remarkably robust to the inclusion of bond disorder – albeit that the transient dynamics approaching the steady states differs qualitatively between the clean and disordered cases – providing an accessible instance of ballistic transport in a disordered setting.