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

arXiv:2610.20724 · cond-mat.stat-mech, quant-ph · Submitted 2026-10-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Long-lived local coherences at high temperature from frozen domain walls".

Mira: The gist Long-lived local coherences at high temperature from frozen domain walls present a mechanism by which transverse spin correlators in quantum-group models can persist anomalously long,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper titled "Long-lived local coherences at high temperature from frozen domain walls". It's about how these things can last way longer than we usually see in chaotic systems.

Mira: Right. The authors are Sarang Gopalakrishnan and Romain Vasseur, and they focus on spin chains that obey a quantum group symmetry. This isn't just any spin chain; it's one with a specific type of symmetry that allows for these long-lived states at high temperature.

Lev: From an engineering standpoint, the big question is whether these results translate to actual hardware. We need to see if we can actually build a system where this quantum group symmetry is active and measure these correlations in our real machines.

Kai: Exactly. The implication here is that we might have a mechanism for preserving quantum information longer than expected when dealing with high-temperature dynamics, which is kind of counter-intuitive in many chaotic models.

Mira: It suggests that the type of symmetry we choose for the system matters immensely; it can lock dynamics into these long-lived modes instead of letting everything dephase quickly.

Lev: If this holds up, it means our error correction schemes might need to account for these specific types of symmetries if we want to get better performance in noisy environments.

The paper's summary: Kai: So what they found in the paper is that these long-lived local coherences can decay at most algebraically, specifically at a rate like one over t squared, or one/t squared <ref:2610.20724#pg1,can decay at most algebraically>.

Mira: That's the key result. They show this is possible for both integrable and chaotic spin chains that have quantum group symmetry, including the XXZ chain. It's not a generic property you get everywhere in these systems.

Lev: If we think about running this on actual hardware, that one/t squared decay rate is pretty slow compared to the exponential decay we often worry about in error correction protocols <ref:2610.20724#pg1>.

Kai: And they use a specific operator, RW, which they say commutes with the Hamiltonian and acts like a spin flip at a local minimum in the height field. This operator keeps the coherence alive for as long as that minimum stays deep enough in its light cone.

Mira: The paper also introduces this concept by decomposing the survival of these correlators into two parts: one is how long a local minimum survives, and another is how fast it moves around.

Lev: That decomposition gives us a way to estimate the generic decay rate as C(t) proportional to t to the negative power of z, which is that spin transport dynamical exponent.

The paper's improvements: Kai: One improvement they focus on is using a "non-undershoot" assumption when applying the Mazur bound derived from the quantum group symmetry. This assumption lets them get a rigorous bound that C(t) can decay at most as fast as one over t squared <ref:2610.20724#pg1>.

Mira: That non-undershoot part is physically motivated, and it's what allows them to say that even in chaotic models, you can still get this algebraic decay bound of one over t squared <ref:2610.20724#pg1>. They also provide explicit calculations for the XXZ chain in the large-anisotropy limit.

Lev: If we were building something, we'd have to worry about that non-undershoot assumption being wrong. That’s where our real hardware simulations would really stress this theoretical finding.

Kai: And they also look at magnetized ensembles, which is a different case where the chaotic models cross over to stretched exponential decay because of the magnetization m.

Mira: They find that for finite magnetization, you get a crossover to stretched exponential dephasing on length scales of about l greater than m minus two. This dependence on the magnetization tells us this quantum group symmetry is quite different from standard SU(two) symmetry <ref:2610.20724#pg1>.

Conclusion: Kai: So to wrap up the paper "Long-lived local coherences at high temperature from frozen domain walls", it confirms that quantum group symmetry provides a mechanism for anomalously long coherence in spin chains, decaying at most as fast as one over t squared.

Mira: It means this isn't just an integrable system feature; it works even in chaotic ones if the quantum group structure is present, and we have to be careful about the assumptions they made about the non-undershoot assumption.

Lev: For us in hardware, this suggests that if we can engineer these quantum group symmetries into our systems, we might find a way to keep coherence alive longer than previously thought when dealing with thermal noise.

Kai: And they show that for finite magnetization, the decay switches over to stretched exponential dephasing on scales related to m minus two, which is a key difference from what you'd expect in simpler models.

Mira: Overall, the paper shows that this specific type of symmetry locks dynamics into these long-lived modes rather than just being a generic feature of the system.

Lev: I think the main thing to watch for is how we can actually realize that quantum group structure robustly enough to harness this effect in a real setting.

Sarang Gopalakrishnan, Romain Vasseur

Department of Electrical and Computer Engineering, Princeton University · Department of Theoretical Physics, University of Geneva · Geneva Quantum Center, University of Geneva

cond-mat.stat-mech, quant-ph

Submitted: 2026-10-14

Updated: 2026-10-14

Comments: 5 pages + supplemental material

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: The gist Long-lived local coherences at high temperature from frozen domain walls present a mechanism by which transverse spin correlators in quantum-group models can persist anomalously long,

Key concepts

Height Representation: This framework describes spin states by mapping each spin orientation (up or down) to a step in a height field. In the presence of quantum group symmetry, local minima in this height field host quantum coherence. This structure is crucial for understanding how information is temporarily protected from dephasing.
Operator RW: This specific operator commutes with the Hamiltonian when restricted to a local region and acts like a spin flip ($\sigma+x$) at a local minimum. Because it acts invisibly to other degrees of freedom, it creates coherence that resists dephasing for timescales related to the depth of the minimum.
Chaotic Model Decay Rate: In chaotic models, transverse correlators are expected to decay as $C(t) \sim t^{-2/z}$, where $z$ is the transport exponent. The paper models this decay by considering two factors: the survival and transport of local minima, which combine to yield this power-law decay rate.
Finite Magnetization Effects: When a net magnetization ($m$) is present, the simple algebraic bound changes. The system exhibits a crossover to stretched-exponential dephasing on scales related to $l \gtrsim m-2$. This demonstrates that quantum group symmetry behaves differently than standard SU(2) symmetry when magnetization is involved.

Terminology

Coherence — 3× in this paper · explained in 2 episodes
Anisotropy — 2× in this paper · explained in 4 episodes
Domain Walls — 1× in this paper · explained in 2 episodes

Summary

The gist Long-lived local coherences at high temperature from frozen domain walls present a mechanism by which transverse spin correlators in quantum-group models can persist anomalously long, decaying at most algebraically like 1/t2, due to a specific role played by quantum group symmetry and the height representation.

Mechanism for Slow Decay

The persistence of these coherences is explained through the height representation where each ↓ (↑) spin maps to a down (up) step in the height field. Under generic quantum evolution, height minima have no special status, but in the presence of quantum group symmetries they host quantum coherence. Specifically, for any window W of the spin chain, there exists an operator RW local to W that commutes with the Hamiltonian HW restricted to W and acts on a product state cx⟩ with a local minimum at x as RW cx⟩ ≈ σ+xcx⟩. The action of σ+x is temporarily invisible to the other degrees of freedom, so they cannot dephase the coherence it creates. This invisibility lasts as long as the minimum in question is the deepest one in its light cone; while it lasts, C(t) is simply related to the return probability of the minimum. In infinite temperature states, a region's minimum typically remains at least l away from any deeper minimum, so spin-flip remains invisible for timescales ≳ l. Together with the power-law decaying return probability of the minimum, this property makes C(t) algebraically long-lived.

Bounds and Limits

The Mazur bound derived from quantum group symmetry suggests that C(t) can decay at most as fast as 1/t2, although this argument is rigorous except for a physically motivated non-undershoot assumption. In the large-anisotropy limit of the XXZ spin chain at infinite temperature, C(t) is explicitly computed to scale as C(t) ∼ √3/(18√t). For general easy-axis anisotropy, the decay rate is estimated to scale as C(t) ∼ t(-2/z), where z is the transport exponent in chaotic models. The finite-size Mazur bound, derived from the overlap of R with E, yields a lower bound C ≥ p 2L x 1 − 2(-L/L/2). This bound reproduces the 4/(π squared L x 2) bound at the center.

XXZ Chain Dynamics

The XXZ spin chain is considered within models obeying a quantum group Uq(sl2) symmetry, which are built from Temperley–Lieb (TL) generators em. The Hamiltonian H(β) encompasses many standard quantum spin chains, including the anisotropic XXZ chain for β = 0. In the folded limit (∆ = ∞), only spin exchanges that preserve the Ising energy remain in slow dynamics, leading to a folded XXZ chain where a flip modifies a frozen pattern. The return probability of the domain wall is estimated as Pret(t) ∼ 2/√4πDt, where D is the infinite-temperature spin diffusion constant. For half filling in the folded chain, C(t) scales as √3/18√J t.

Chaotic Models and String Hierarchy

In chaotic models (β ≠ 0), the transverse correlator is expected to decay as C(t) ∼ t(-2/z). Heuristically, this is estimated as C(t) ≃ ρw(t)Pret(t) ∼ t(-2/z), where ρ is the probability that σ+ attaches to a height minimum, w(t) is the survival probability of that minimum, and Pret(t) is the probability that the minimum returns to its original position at time t. For finite anisotropy away from ∆ = ∞, s-strings describe bound states of s spin flips with an intrinsic hopping scale γs ∼ Jq(1-s). The coherence time is estimated as τs ∼ t0e ηs, leading to a decay rate C(t) ≃ Pret(t) X s w(t) ∼ 1/(pD(∆))t ln q ln(t/t0) squared.

Finite Magnetization Effects

When considering infinite-temperature product-state ensembles with net magnetization density = m, the Mazur bound becomes trivial for any m ≠ 0 because the height minimum is overwhelmingly likely to occur at the region’s edge. In chaotic chains, a crossover to stretched-exponential dephasing occurs on length scales l ≳ m−2, or timescales t ≳ m−2z. This sensitivity to m illustrates that the quantum group symmetry is sharply distinct from conventional SU(2) symmetry.

Conclusion

The slow decay of transverse correlators is not generic for integrable systems, and the mechanism relies purely on a quantum-group symmetry locking dynamics to a hydrodynamic mode rather than conventional integrability. The results show that C(t) remains above the algebraic bound in both integrable XXZ and chaotic quantum-group chains. Furthermore, for finite magnetization, the decay is governed by exponential factors related to the magnetization µ = artanh m.

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Improvements for AI systems

A quantum-group symmetry framework allows AI systems to maintain anomalously long local coherences in chaotic many-body systems, specifically by utilizing an operator RW that (i) commutes with the Hamiltonian HW restricted to the window, and (ii) acts on a product state cx⟩ with a local minimum at x as RW cx⟩ ≈ σ+xcx⟩. This enables AI to persist information across timescales that would otherwise cause rapid dephasing.
The system can compute an algebraic lower bound for the transverse spin autocorrelation function, stating C(t) ≳ 1/t squared, which is proven for all q ≥ 1 using the canonical polar factor and Griffiths-type correlation inequalities. This provides a rigorous, non-exponential decay estimate for coherence in chaotic models.
The AI can model complex spin chain dynamics by decomposing survival into two components: the survival and transport of local minima, allowing it to estimate the generic decay rate as C(t) ≃ t-2/z in chaotic models, where z is the spin transport dynamical exponent.
The system can perform long-time correlator analysis by employing a non-undershoot assumption, ensuring that the smoothed correlator C˜W(t) remains above its plateau before boundary effects become appreciable, leading to the bound C˜(t) ≥ Bl − ϵ(l, 2t) = 1 + o(1/4π2v 2t 2).
The AI can analyze finite magnetization ensembles by predicting a crossover to stretched-exponential dephasing on length scales where lations of size l≳ m−2, allowing for the prediction of decay rates like C(t) ∼ t-1/2 - 2μ/ln q.

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) σ-x(t) σ+ x(0) can decay at most algebraically: C(t) 1/t squared. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute C(t) about 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) about t-2/z (for transport exponent z) in the chaotic models.