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:2609.37512

Exact anomalous current fluctuations in the strong-anisotropy limit of the XXZ chain

Taiki Ishiyama, Taiga Kurose, Kazuya Fujimoto, Tomohiro Sasamoto

cond-mat.stat-mechcond-mat.quant-gasmath-phquant-phSubmitted Sep 29, 2026• Announced Sep 30, 2026• 0 citations
arXivHTMLPDF

Abstract

We study spin-current fluctuations of the folded XXZ chain, which describes the strong-anisotropy limit of the XXZ chain. We obtain an exact expression for the moment-generating function of the time-integrated spin current at infinite temperature. A long-time asymptotic analysis establishes that the rescaled time-integrated current converges to a non-Gaussian distribution described by the M-Wright function. The derivation relies on a nonlocal map to the one-dimensional t-0 model and its exact spin-charge separation. By extending this approach, we also show that the dynamical correlation function of the spins summed over two adjacent sites exhibits a diffusive Gaussian profile at long times.

Related papers

Anomalous Hydrodynamic Fluctuations in the Quantum XXZ Spin Chain

Takato Yoshimura, Žiga Krajnik, Alvise Bastianello +1 more

The quantum XXZ spin-1/2 chain features non-Gaussian spin current fluctuations in the regime of easy-axis anisotropy. Using ballistic macroscopic fluctuation theory, we derive the exact asymptotic probability distribution of typical spin-current fluctuations in thermal equilibrium at zero average magnetization. The obtained nested Gaussian distribution is fully characterized by its variance, which we analytically relate to the spin diffusion constant and static spin susceptibility, comparing our prediction with numerical simulations. By unveiling how the same mechanism which leads to anomalous charge current fluctuations in single-file systems manifests itself in the XXZ chain, our approach establishes the universal hydrodynamic origin of the observed anomalous fluctuations.

arXiv:2602.24242•Physical Review Letters•Jul 22, 2026•0 citations

Exact Anomalous Current Fluctuations in Quantum Many-Body Dynamics

Kazuya Fujimoto, Taiki Ishiyama, Taiga Kurose +2 more

Fluctuations of integrated currents have attracted considerable interest over the past decades in the context of statistical mechanics. Recently, anomalous current fluctuations, characterized by the M-Wright function, were obtained exactly in a classical automaton [$Ž$. Krajnik et al., Phys. Rev. Lett. 128, 160601 (2022)], and previous studies have shown that the anomalous behavior can arise in a variety of classical systems. Despite the rapidly growing interest in such anomalous behaviors, which capture a universal aspect of one-dimensional many-body transport, the exact derivation of the M-Wright function in quantum many-body systems has remained elusive. In this Letter, we present the first exact microscopic derivation of the M-Wright function in quantum many-body dynamics by analyzing the integrated spin current in a one-dimensional Fermi-Hubbard model with infinitely strong repulsive interactions. Our results lay the groundwork for exploring anomalous integrated currents in a broad class of quantum many-body systems.

cond-mat.stat-mechCross-listedarXiv:2602.24008•Physical Review Letters•Mar 2, 2026•0 citations

Magnetization dynamics in clean and disordered spin-1 XXZ chains

Jonas Richter, Niklas Casper, Wolfram Brenig +1 more

We study spin transport in the one-dimensional anisotropic $S=1$ Heisenberg model. Particular emphasis is given to dynamics at infinite temperature, where current autocorrelations and spatiotemporal correlation functions are obtained by means of an efficient pure-state approach based on the concept of typicality. Our comprehensive numerical analysis unveils that high-temperature spin transport is diffusive in the easy-axis regime for strong exchange anisotropies. This finding is based on the combination of numerous signatures, such as (i) Gaussian spreading of correlations, (ii) a time-independent diffusion coefficient, (iii) power-law decay of equal-site correlations, (iv) exponentially decaying long-wavelength modes, and (v) Lorentzian line shapes of the dynamical structure factor. Moreover, we provide evidence that some of these signatures are not exclusively restricted to the infinite-temperature limit but can persist at lower temperatures as well, where we complement our results by additional quantum Monte Carlo simulations of large systems. In contrast to the easy-axis regime, we show that in the case of an isotropic chain, the signatures (i)--(v) are much less pronounced or even entirely absent, suggesting the existence of anomalous spin transport despite the nonintegrability of the model. Eventually, upon introducing a random on-site magnetic field, we observe a breakdown of diffusion and distinctly slower dynamics. In particular, our results exhibit qualitative similarities to disordered spin-$1/2$ chains and might be consistent with the onset of many-body localization in the $S=1$ model for sufficiently strong disorder.

arXiv:1907.03004•Physical review. B./Physical review. B•Oct 15, 2019•21 citations

Spin diffusion and the spin-1/2 XXZ chain at T=∞ from exact diagonalization

K. Fabricius, Barry M. McCoy

We study the long time behavior of the $\mathrm{zz}$ and $\mathrm{xx}$ time-dependent autocorrelation function of the spin-1/2 $\mathrm{XXZ}$ chain at $T=\ensuremath{\infty}$ by exact diagonalizations on a chain of 16 sites. We find that the numerical results for the $\mathrm{zz}$ correlation are very well fit by the formula ${t}^{\ensuremath{-}d}[{A+Be}^{\ensuremath{-}\ensuremath{\gamma}(t\ensuremath{-}{t}_{0})}\mathrm{cos}\ensuremath{\Omega}(t\ensuremath{-}{t}_{0})].$ From this we estimate $d$ as a function of the anisotropy of the chain and study the crossover from ballistic to diffusive behavior.

arXiv:cond-mat/9711146•Physical review. B, Condensed matter•Apr 1, 1998•77 citations

Full distribution and large deviations of local observables in an exactly solvable current-carrying steady state of a strongly driven X X Z chain

Sandipan Manna, G. J. Sreejith

Current-carrying steady states of interacting spin chains exhibit rich structures generated through an interplay of constraints from the Hamiltonian dynamics and those induced by the current. The XXZ spin chain when coupled to maximally polarizing Lindblad terms (with opposite signs on either end) admits an exact solution for the steady state in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of local spin observables in the nonequilibrium steady state. We present exact expressions for spin correlators, entropy per site, and scaled cumulant generating functions (SCGF) for distributions of local observables in the XX limit (Ising anisotropy Δ=0). Further, we use the exact MPS solution in the Δ>0 regime to calculate numerically exact entropy, correlations, as well as full distributions of spin observables in large systems. In systems where Δ is a cosine of rational multiple of π, we can numerically exactly estimate the large system limit of the SCGF and the large deviation/rate functions of local-z magnetization. For these, we show that the deviations of the SCGF, calculated in finite systems, from the asymptotic large system size limit decay exponentially with system size; however, the decay rate is a discontinuous function of Δ. The x magnetization density shows a double peak structure at Δ≲1, suggesting short-range ferromagnetic ordering in the x direction similar to what was reported for the ground state of the XXZ chain.

arXiv:2409.10458•Physical review. E•Apr 28, 2025•0 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
We study spin-current fluctuations of the folded XXZ chain, which describes the strong-anisotropy limit of the XXZ chain. We obtain an exact expression for the moment-generating function of the time-integrated spin current at infinite temperature. A long-time asymptotic analysis establishes that the rescaled time-integrated current converges to a non-Gaussian distribution described by the M-Wright function. The derivation relies on a nonlocal map to the one-dimensional t-0 model and its exact spin-charge separation. By extending this approach, we also show that the dynamical correlation function of the spins summed over two adjacent sites exhibits a diffusive Gaussian profile at long times.
The quantum XXZ spin-1/2 chain features non-Gaussian spin current fluctuations in the regime of easy-axis anisotropy. Using ballistic macroscopic fluctuation theory, we derive the exact asymptotic probability distribution of typical spin-current fluctuations in thermal equilibrium at zero average magnetization. The obtained nested Gaussian distribution is fully characterized by its variance, which we analytically relate to the spin diffusion constant and static spin susceptibility, comparing our prediction with numerical simulations. By unveiling how the same mechanism which leads to anomalous charge current fluctuations in single-file systems manifests itself in the XXZ chain, our approach establishes the universal hydrodynamic origin of the observed anomalous fluctuations.
Fluctuations of integrated currents have attracted considerable interest over the past decades in the context of statistical mechanics. Recently, anomalous current fluctuations, characterized by the M-Wright function, were obtained exactly in a classical automaton [ZˇŽZˇ. Krajnik et al., Phys. Rev. Lett. 128, 160601 (2022)], and previous studies have shown that the anomalous behavior can arise in a variety of classical systems. Despite the rapidly growing interest in such anomalous behaviors, which capture a universal aspect of one-dimensional many-body transport, the exact derivation of the M-Wright function in quantum many-body systems has remained elusive. In this Letter, we present the first exact microscopic derivation of the M-Wright function in quantum many-body dynamics by analyzing the integrated spin current in a one-dimensional Fermi-Hubbard model with infinitely strong repulsive interactions. Our results lay the groundwork for exploring anomalous integrated currents in a broad class of quantum many-body systems.
We study spin transport in the one-dimensional anisotropic S=1S=1S=1 Heisenberg model. Particular emphasis is given to dynamics at infinite temperature, where current autocorrelations and spatiotemporal correlation functions are obtained by means of an efficient pure-state approach based on the concept of typicality. Our comprehensive numerical analysis unveils that high-temperature spin transport is diffusive in the easy-axis regime for strong exchange anisotropies. This finding is based on the combination of numerous signatures, such as (i) Gaussian spreading of correlations, (ii) a time-independent diffusion coefficient, (iii) power-law decay of equal-site correlations, (iv) exponentially decaying long-wavelength modes, and (v) Lorentzian line shapes of the dynamical structure factor. Moreover, we provide evidence that some of these signatures are not exclusively restricted to the infinite-temperature limit but can persist at lower temperatures as well, where we complement our results by additional quantum Monte Carlo simulations of large systems. In contrast to the easy-axis regime, we show that in the case of an isotropic chain, the signatures (i)--(v) are much less pronounced or even entirely absent, suggesting the existence of anomalous spin transport despite the nonintegrability of the model. Eventually, upon introducing a random on-site magnetic field, we observe a breakdown of diffusion and distinctly slower dynamics. In particular, our results exhibit qualitative similarities to disordered spin-1/21/21/2 chains and might be consistent with the onset of many-body localization in the S=1S=1S=1 model for sufficiently strong disorder.
We study the long time behavior of the zz\mathrm{zz}zz and xx\mathrm{xx}xx time-dependent autocorrelation function of the spin-1/2 XXZ\mathrm{XXZ}XXZ chain at $T=\ensuremath{\infty}$ by exact diagonalizations on a chain of 16 sites. We find that the numerical results for the zz\mathrm{zz}zz correlation are very well fit by the formula ${t}^{\ensuremath{-}d}[{A+Be}^{\ensuremath{-}\ensuremath{\gamma}(t\ensuremath{-}{t}_{0})}\mathrm{cos}\ensuremath{\Omega}(t\ensuremath{-}{t}_{0})].$ From this we estimate ddd as a function of the anisotropy of the chain and study the crossover from ballistic to diffusive behavior.
Current-carrying steady states of interacting spin chains exhibit rich structures generated through an interplay of constraints from the Hamiltonian dynamics and those induced by the current. The XXZ spin chain when coupled to maximally polarizing Lindblad terms (with opposite signs on either end) admits an exact solution for the steady state in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of local spin observables in the nonequilibrium steady state. We present exact expressions for spin correlators, entropy per site, and scaled cumulant generating functions (SCGF) for distributions of local observables in the XX limit (Ising anisotropy Δ=0). Further, we use the exact MPS solution in the Δ>0 regime to calculate numerically exact entropy, correlations, as well as full distributions of spin observables in large systems. In systems where Δ is a cosine of rational multiple of π, we can numerically exactly estimate the large system limit of the SCGF and the large deviation/rate functions of local-z magnetization. For these, we show that the deviations of the SCGF, calculated in finite systems, from the asymptotic large system size limit decay exponentially with system size; however, the decay rate is a discontinuous function of Δ. The x magnetization density shows a double peak structure at Δ≲1, suggesting short-range ferromagnetic ordering in the x direction similar to what was reported for the ground state of the XXZ chain.
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.