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arXiv:2604.27074

Long-lived local quantum coherences from hydrodynamic large deviations

Ewan McCulloch, J. Alexander Jacoby, Sarang Gopalakrishnan

quant-phcond-mat.stat-mechcond-mat.str-elhep-thSubmitted Apr 29, 2026• Announced May 1, 2026• 0 citations• Revised Sep 14, 2026 (v2)
v1 · Apr 29, 2026v2 · Sep 14, 2026
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Abstract

We develop a framework to describe how quantum coherences between distinct charge sectors evolve under generic charge-conserving dynamics. Our framework captures the nonperturbative interactions between quantum coherences and hydrodynamic large deviations---i.e., rare ``voids'' of low charge entropy. Conditional on surviving, the quantum coherence and its surrounding void form a collective polaron-like object. In one dimension, even at infinite temperature, we show that the lifetime of coherences is parametrically enhanced because they bind to voids. We use our framework to address two fundamental questions about generic quantum dynamics with a conserved charge. First, we argue that gapped Ruelle-Pollicott resonances are absent in the weak-noise limit, even in sectors of operator space that contain no hydrodynamic slow modes: instead, the spectral gap in all sectors vanishes nonperturbatively in the noise strength. Second, we compute the spacetime asymptotics of the dynamical single-particle Green's function, both in the weak-noise regime and in the absence of noise. In the noiseless case, we find that the void--coherence polaron undergoes subdiffusion, with an exponent we calculate. We support our general arguments with a microscopic derivation for random charge-conserving circuits, as well as numerical evidence from tensor-network simulations.

Comments
51 pages, 13 figures

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We develop a framework to describe how quantum coherences between distinct charge sectors evolve under generic charge-conserving dynamics. Our framework captures the nonperturbative interactions between quantum coherences and hydrodynamic large deviations---i.e., rare ``voids'' of low charge entropy. Conditional on surviving, the quantum coherence and its surrounding void form a collective polaron-like object. In one dimension, even at infinite temperature, we show that the lifetime of coherences is parametrically enhanced because they bind to voids. We use our framework to address two fundamental questions about generic quantum dynamics with a conserved charge. First, we argue that gapped Ruelle-Pollicott resonances are absent in the weak-noise limit, even in sectors of operator space that contain no hydrodynamic slow modes: instead, the spectral gap in all sectors vanishes nonperturbatively in the noise strength. Second, we compute the spacetime asymptotics of the dynamical single-particle Green's function, both in the weak-noise regime and in the absence of noise. In the noiseless case, we find that the void--coherence polaron undergoes subdiffusion, with an exponent we calculate. We support our general arguments with a microscopic derivation for random charge-conserving circuits, as well as numerical evidence from tensor-network simulations.
Chaotic quantum systems at finite entropy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. We argue that in fact this dephasing is generically subexponential in one-dimensional systems with conservation laws: all local correlation functions decay as exp[-O(t^{α})] with 0≤α≤2/3, even when the operators are orthogonal to all hydrodynamic modes. The mechanism is diffusion-limited dephasing, in which rare low-entropy regions ("voids") protect quantum coherences. This intrinsically quantum effect lies beyond standard hydrodynamics and disappears under extrinsic dephasing. In random charge-conserving circuits we find α=1/2, while in generic translation-invariant Floquet systems we bound α≤2/3. Our arguments are general, subject principally to the assumption that thermal fluctuations can create regions of zero entropy density. In systems with energy conservation, this assumption is automatically satisfied because of the third law of thermodynamics.
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.
We consider the dynamics of generic chaotic quantum many-body systems with no conservation laws, subject to weak bulk dissipation. It was recently observed [T. Mori, Phys. Rev. B 109, 064311 (2024)] that the generator of these dissipative dynamics, a quantum channel E\mathcal{E}E, retains a nonzero gap as the dissipation strength $\ensuremath{\gamma}\ensuremath{\rightarrow}0$ if the thermodynamic limit is taken first. We use a hydrodynamic description of operator spreading in the presence of dissipation to estimate the gap of E\mathcal{E}E as $\ensuremath{\gamma}\ensuremath{\rightarrow}0$, to calculate the operator-size distribution of the slowest eigenmodes of E\mathcal{E}E, and to relate the gap to the long-time decay rates of autocorrelation functions under unitary Floquet dynamics. We provide a microscopic derivation of this hydrodynamic perspective for random unitary circuits. We argue that the gap in the $\ensuremath{\gamma}\ensuremath{\rightarrow}0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics.
We study the single-particle Green's function G(x,t)=⟨σx−(0)σ0+(t)⟩G(x,t)=\langle σ^-_x(0)σ^+_0(t)\rangleG(x,t)=⟨σx−​(0)σ0+​(t)⟩ in one-dimensional particle-number-conserving random unitary circuits coupled to an external bath. For fixed spacetime disorder, we argue that G(x,t)G(x,t)G(x,t) is governed, in both the strong- and weak-noise limits, by directed waves in a random medium. We find Kardar-Parisi-Zhang (KPZ) scaling in the wandering statistics of the normalized spatial distribution p(x,t)∝∣G(x,t)∣2p(x,t)\propto |G(x,t)|^2p(x,t)∝∣G(x,t)∣2 and in the associated free energy. In particular, its center ⟨x(t)⟩≡∑xx p(x,t)\langle x(t)\rangle\equiv\sum_x x\, p(x,t)⟨x(t)⟩≡∑x​xp(x,t) wanders on a length-scale O(t2/3)\mathcal{O}(t^{2/3})O(t2/3), while sample-to-sample fluctuations of −log⁡∑x∣G(x,t)∣2-\log\sum_x |G(x,t)|^2−log∑x​∣G(x,t)∣2 scale as t1/3t^{1/3}t1/3. At weak noise γ≪1γ\ll 1γ≪1, the crossover to the strong-disorder fixed point occurs at a parametrically long time O(γ−3/2)\mathcal{O}(γ^{-3/2})O(γ−3/2). These predictions are confirmed numerically using tensor-network simulations of the noisy operator dynamics in individual circuits at moderate noise, and of a phase-annealed proxy retaining hopping disorder at weak noise.
We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on U(1)U(1)U(1)-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences both globally, via the participation entropy, and locally, via the relative entropy of coherence. Combining exact vector evolution, matrix product state simulations, and replica tensor networks methods, we find that conservation laws replace the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of the global coherence measures. Locally, symmetry-constrained circuits show a clean rise-peak-fall structure whose peak time grows algebraically with subsystem size. In contrast, ergodic Hamiltonians broaden the peak into an extended plateau at larger subsystems, highlighting a qualitatively distinct mechanism. Coherence thus emerges as a sensitive probe of symmetry-constrained thermalization, linking quantum resource dynamics to many-body transport.
The scrambling of quantum information in closed many-body systems, as measured by out-of-timeordered correlation functions (OTOCs), has received considerable attention lately.Recently, a hydrodynamical description of OTOCs has emerged from considering random local circuits.Numerical work suggests that aspects of this description are universal to ergodic many-body systems, even without randomness; a conjectured explanation for this is that while the random circuits have noise built into them, deterministic quantum systems, much like classically chaotic ones, "generate their own noise" and look effectively random on sufficient length scales and timescales.In this paper, we extend this approach to systems with locally conserved quantities (e.g., energy).We do this by considering local random unitary circuits with a conserved U(1) charge and argue, with numerical and analytical evidence, that the presence of a conservation law slows relaxation in both time-ordered and out-of-time-ordered correlation functions; both can have a diffusively relaxing component or "hydrodynamic tail" at late times.We verify the presence of such tails also in a deterministic, periodically driven system.We show that for OTOCs, the combination of diffusive and ballistic components leads to a wave front with a specific asymmetric shape, decaying as a power law behind the front.These results also explain existing numerical investigations in non-noisy ergodic systems with energy conservation.Moreover, we consider OTOCs in Gibbs states, parametrized by a chemical potential μ, and apply perturbative arguments to show that for μ ≫ 1 the ballistic front of information spreading can only develop at times exponentially large in μ-with the information traveling diffusively at earlier times.We also develop a new formalism for describing OTOCs and operator spreading, which allows us to interpret the saturation of OTOCs as a form of thermalization on the Hilbert space of operators.