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:1302.5509 · Physical Review Letters

Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder

Marko Žnidarič

Published Feb 12, 2013• 62 citations
arXivHTMLPDF

Abstract

We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is found to be diffusive. This shows that (i) quantum chaotic systems can possess ballistic subspaces, and (ii) diffusive and ballistic transport modes can coexist in a rather simple nonintegrable model. In the limit of an infinite anisotropy in rungs the system studied is equivalent to the one-dimensional Hubbard model.

DOI
10.1103/physrevlett.110.070602

Related papers

Transport control in low-dimensional spin- 1∕2 Heisenberg systems

Léa Ferreira dos Santos

We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.

arXiv:0805.4045•Physical Review E•Sep 19, 2008•21 citations

Coexistence of diffusive and ballistic transport in integrable quantum lattice models

Peter Prelovšek, Marcin Mierzejewski, J. Herbrych

We investigate the high-temperature dynamical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusivelike transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\ensuremath{\le}32$ sites for the XXZ spin model with the frequency resolution $\ensuremath{\delta}\ensuremath{\omega}\ensuremath{\sim}{10}^{\ensuremath{-}3}J$. Results for the XXZ chain reveal a fine structure of $\ensuremath{\sigma}(\ensuremath{\omega})$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\mathrm{\ensuremath{\Delta}}$. Still, we do not find clear evidence for a diffusive component, at least not for commensurate values of $\mathrm{\ensuremath{\Delta}}$, particularly for $\mathrm{\ensuremath{\Delta}}=0.5$, as well as for $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.

arXiv:2107.02454•Physical review. B./Physical review. B•Sep 28, 2021•14 citations

Can diffusive and ballistic transport coexist in integrable quantum lattice models

Peter Prelovšek, Marcin Mierzejewski, J. Herbrych

We investigate the high-temperature dynamical conductivity $\sigma(\omega)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusive-like transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\leq 32$ sites for XXZ spin model with the frequency resolution $\delta \omega \sim 10^{-3} J$. Results for the XXZ chain reveal a fine structure of $\sigma(\omega)$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\Delta$. Still, we do not find a clear evidence for a diffusive component, at least not for commensurate values of $\Delta$, particularly for $\Delta =0.5$, as well as for $\Delta \to 0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.

•Jul 6, 2021•0 citations

Magnetization transport in spin ladders and next-nearest-neighbor chains

Marko Žnidarič

We study magnetization transport at infinite temperature in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero average magnetization, while numerical simulations of a nonequilibrium stationary setting indicate an anomalous transport in the zero-magnetization sector. For other systems, isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion typical of quantum chaotic systems, numerical simulations indicate diffusive transport.

arXiv:1304.2171•Physical Review B•Nov 25, 2013•30 citations

Absence of finite-temperature ballistic charge (and spin) transport in the 1D Hubbard model at half filling (and zero spin density)

J. M. P. Carmelo, Shi-Jian Gu, M J Sampaio

Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness D η ( T ) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness D s ( T ) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems.

Journal of Physics A Mathematical and Theoretical•Jun 9, 2014•1 citation

Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model

Thomas Iadecola, Marko Žnidarič

We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.

arXiv:1811.07903•Physical Review Letters•Jul 16, 2019•92 citations
We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is found to be diffusive. This shows that (i) quantum chaotic systems can possess ballistic subspaces, and (ii) diffusive and ballistic transport modes can coexist in a rather simple nonintegrable model. In the limit of an infinite anisotropy in rungs the system studied is equivalent to the one-dimensional Hubbard model.
We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.
We investigate the high-temperature dynamical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusivelike transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\ensuremath{\le}32$ sites for the XXZ spin model with the frequency resolution $\ensuremath{\delta}\ensuremath{\omega}\ensuremath{\sim}{10}^{\ensuremath{-}3}J$. Results for the XXZ chain reveal a fine structure of $\ensuremath{\sigma}(\ensuremath{\omega})$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\mathrm{\ensuremath{\Delta}}$. Still, we do not find clear evidence for a diffusive component, at least not for commensurate values of $\mathrm{\ensuremath{\Delta}}$, particularly for $\mathrm{\ensuremath{\Delta}}=0.5$, as well as for $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.
We investigate the high-temperature dynamical conductivity σ(ω)\sigma(\omega)σ(ω) in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusive-like transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to L≤32L\leq 32L≤32 sites for XXZ spin model with the frequency resolution δω∼10−3J\delta \omega \sim 10^{-3} Jδω∼10−3J. Results for the XXZ chain reveal a fine structure of σ(ω)\sigma(\omega)σ(ω) spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter Δ\DeltaΔ. Still, we do not find a clear evidence for a diffusive component, at least not for commensurate values of Δ\DeltaΔ, particularly for Δ=0.5\Delta =0.5Δ=0.5, as well as for Δ→0\Delta \to 0Δ→0. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.
We study magnetization transport at infinite temperature in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero average magnetization, while numerical simulations of a nonequilibrium stationary setting indicate an anomalous transport in the zero-magnetization sector. For other systems, isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion typical of quantum chaotic systems, numerical simulations indicate diffusive transport.
Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness D η ( T ) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness D s ( T ) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems.
We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.