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arXiv:2610.20724

Long-lived local coherences at high temperature from frozen domain walls

Sarang Gopalakrishnan, Romain Vasseur

cond-mat.stat-mechquant-phSubmitted Oct 14, 2026• Announced Oct 16, 2026• 0 citations
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Abstract

Local coherences between distinct charge sectors--measured by the single-particle Green's function or the transverse spin autocorrelation function--do not overlap with hydrodynamic modes. At finite temperature, therefore, they decay faster than any power law in generic chaotic systems. We present a mechanism by which these coherences can persist anomalously long, for integrable and chaotic spin chains (including the XXZ and Fredkin spin chains) that obey a quantum group symmetry. We show--using a Mazur bound derived from the quantum-group symmetry, together with locality and a "non-undershoot" assumption--that the transverse spin autocorrelation function $C(t) \equiv \langle σ^-_x(t) σ^+_x(0)\rangle$ can decay at most algebraically: $C(t) \gtrsim 1/t^2$. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute $C(t) \sim \sqrt{3}/(18 \sqrt{t})$. We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as $C(t) \sim t^{-2/z}$ (for transport exponent $z$) in the chaotic models.

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5 pages + supplemental material

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Local coherences between distinct charge sectors--measured by the single-particle Green's function or the transverse spin autocorrelation function--do not overlap with hydrodynamic modes. At finite temperature, therefore, they decay faster than any power law in generic chaotic systems. We present a mechanism by which these coherences can persist anomalously long, for integrable and chaotic spin chains (including the XXZ and Fredkin spin chains) that obey a quantum group symmetry. We show--using a Mazur bound derived from the quantum-group symmetry, together with locality and a "non-undershoot" assumption--that the transverse spin autocorrelation function C(t)≡⟨σx−(t)σx+(0)⟩C(t) \equiv \langle σ^-_x(t) σ^+_x(0)\rangleC(t)≡⟨σx−​(t)σx+​(0)⟩ can decay at most algebraically: C(t)≳1/t2C(t) \gtrsim 1/t^2C(t)≳1/t2. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute C(t)∼3/(18t)C(t) \sim \sqrt{3}/(18 \sqrt{t})C(t)∼3​/(18t​). We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as C(t)∼t−2/zC(t) \sim t^{-2/z}C(t)∼t−2/z (for transport exponent zzz) in the chaotic models.
The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics -- such as superdiffusion -- in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying U(1)U(1)U(1) charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.
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.
The conventional wisdom suggests that transports of conserved quantities in nonintegrable quantum many-body systems at high temperatures are diffusive. Recent study suggests a potential counterexample of this paradigm. We independently complement this counterexample by directly uncovering anomalous infinite-temperature hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. This model, classified as nonintegrable due to its Wigner-Dyson level-spacing statistics in the random matrix theory, exhibits a surprising superdiffusive-ballistic-superdiffusive transport transition by varying the power-law exponent of couplings for a fixed anisotropy. Our findings are verified by multiple observables, including the spin-spin autocorrelator, mean-square displacement, and spin conductivity. Interestingly, we further quantify the degree of quantum chaos using the Kullback-Leibler divergence between the entanglement entropy distributions of the model's eigenstates and a random state. Remarkably, an observed local maximum in the divergence near the transition boundary suggests a link between anomalous hydrodynamics and a suppression of quantum chaos. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of nonintegrable quantum many-body systems.
The decay of (disorder-averaged) static spin correlation functions at T = 0 for the one-dimensional spin-1/2 XXZ antiferromagnet with uniform longitudinal coupling J ∆ and random transverse coupling Jλi is investigated by numerical calculations for ensembles of finite chains. At ∆ = 0 (XX model) the calculation is based on the Jordan-Wigner mapping to free lattice fermions for chains with up to N = 100 sites. At ∆ ̸ = 0 Lanczos diagonalizations are carried out for chains with up to N = 22 sites. The longitudinal correlation function 〈Sz 0Sz r 〉 is found to exhibit a power-law decay with an exponent that varies with ∆ and, for nonzero ∆, also with the width of the λi-distribution. The results for the transverse correlation function 〈S x 0 Sx r 〉 show a crossover from power-law decay to exponential decay as the exchange disorder is turned on. 1 Typeset using REVTEXThe combination of randomness and quantum fluctuations is well-known to be a fertile ground for interesting physical phenomena including Anderson localization. In onedimensional (1D) tight-binding systems the rule is that disorder always leads to localization. However, if the randomness is purely off-diagonal, the localization length diverges at the band center, 1 which is bound to affect the decay law of correlation functions. One particular off-diagonally disordered fermion model, the 1D half-filled tight-binding model with random hopping, is equivalent to the special XX case ( ∆ = 0) of the 1D s = 1/2 XXZ model with random transverse exchange coupling, described by the Hamiltonian H = J ∑
Abstract We consider the integrable one-dimensional spin-1 chain defined by the Zamolodchikov–Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-1/2 model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-1 Babujian–Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-1 ZF chain. Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded. Using the Mazur inequality, we show that, as for the XXZ model, these quasi-local charges are enough to prove that the high-temperature spin Drude weight is non-vanishing in the thermodynamic limit, thus establishing ballistic spin transport at high temperature.
We introduce and implement a reformulation of the strong-disorder renormalization group method in real space, well suited to study bond-disordered antiferromagnetic power-law coupled quantum spin chains. We apply it to a chain of randomly placed spins coupled by power-law long-range interaction with power $\ensuremath{\alpha}$. First, keeping only interactions between adjacent spins, we derive the Master equation and confirm that it is solved by the infinite randomness fixed-point distribution. Then, we derive the master equation for power-law long-range interaction between all spins for any anisotropy $\ensuremath{\gamma}$ ranging from the XX limit, $\ensuremath{\gamma}=0$, to the isotropic Heisenberg limit, $\ensuremath{\gamma}=1,$ which corresponds to a tight-binding chain of disordered long-range interacting fermions with long-range hopping. We thereby show that the distribution function of couplings JJJ smaller than renormalization scale $\mathrm{\ensuremath{\Omega}}$ flows to the strong-disorder fixed-point distribution of finite width $2\ensuremath{\alpha}.$ We find only small corrections to that distribution, which depend on power exponent $\ensuremath{\alpha}$ and coupling anisotropy $\ensuremath{\gamma}.$ As a consequence, the low-temperature magnetic susceptibility diverges with an anomalous power law. The distribution of singlet lengths lll is found to decay as ${l}^{\ensuremath{-}2}$. The entanglement entropy of a subsystem of length nnn increases in the ground state logarithmically for all $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$. After a global quantum quench, the entanglement entropy increases with time logarithmically as $S(t)\ensuremath{\sim}ln(t)/(2\ensuremath{\alpha})$.