Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2211.10451

Quantum-classical correspondence of strongly chaotic many-body spin models

Luis Benet·Fausto Borgonovi·Felix M. Izrailev·Lea F. Santos
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of individual spins. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent that determines the local instability of each individual spin moving under the influence of all other spins. Within this picture, we introduce a rigorous and simple test of ergodicity for the spin motion, and use it to identify when classical chaos is both strong and global in phase space. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos as a function of the model parameters. From the comparison between the quantum and classical domains, we demonstrate that quantum quantities, such as the local density of states (LDOS) and the shape of the chaotic eigenfunctions written in the non-interacting many-body basis, have well-defined classical counterparts. Another central finding is the relationship between the Kolmogorov-Sinai entropy and the width of the LDOS, which is useful for studies of many-body dynamics.

Explore related subjects

cond-mat.stat-mechquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Luis Benet, Fausto Borgonovi, Felix M. Izrailev, Lea F. Santos. 2022-11-18. Quantum-classical correspondence of strongly chaotic many-body spin models. https://doi.org/10.1103/physrevb.107.155143

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Machine learning topological defect formation: When are the defects made?

Topological defects that form in a nonequilibrium second-order phase transition are presumably seeded by fluctuations of the order parameter in the vicinity of the critical point. Motivated by this conjecture that underlies the Kibble-Zurek mechanism (KZM), we investigate whether machine learning (ML) can anticipate their locations from the fluctuations in the ``impulse regime'', the time interval when the evolution of the order parameter cannot keep up with the conditions imposed by the quench. Going beyond the conventional KZM focus on defect density, we show that a recurrent neural network can predict locations of topological defects from short-time dynamical data deep within the impulse regime. We thus demonstrate that defects are sown in the immediate vicinity of the critical point. The seeds of defects, fluctuations imprinted on the evolving order parameter, are exponentially small near the critical point, but become amplified by the evolution and play a dominant role in breaking symmetry. This is before the freezeout time that concludes the impulse regime, and well before the order parameter assumes its final symmetry-broken configuration. Furthermore, we find that the predictive power of the ML also exhibits power-law scaling consistent with KZM.

cond-mat.stat-mech↗
arXiv2026

Long-lived memory in sliding spin chains

We study a system of two ferromagnetic one-dimensional Ising chains coupled to a thermal bath, which are driven out of equilibrium by being moved past one another at a constant speed. We show that even at modest speeds, magnetic friction between the two chains significantly increases the ability of the system to order. In particular, at inverse temperature $β$, Ising coupling $J$, and sliding speed $v$, the dynamics retains memory of its initial magnetization for a time that increases from $\exp(O(βJ))$ at $v = 0$ to $\exp(O((\b J)^2v))$ when $v>v_c$, where $v_c$ is a small constant. Magnetic friction thus provides a simple mechanism for parametrically slowing down thermalization in a one-dimensional magnet.

cond-mat.stat-mech↗
arXiv2026

Nonequilibrium corrections to conserved Ising criticality in scalar active matter: Ward identities, spectrum, and long crossovers

We identify the slowest-decaying nonequilibrium perturbations near the three-dimensional conserved Ising critical point and determine their impact on finite-size observables. We study two classes of perturbations: a field-dependent noise-to-mobility ratio $Θ(ϕ)=D(ϕ)/M(ϕ)$ and the gradient activity of Active Model B+. Starting from the Martin-Siggia-Rose-Janssen-De Dominicis action, we compute the linearized flow using the functional renormalization group. The transport sector is block triangular, with leading odd eigenvalue $y_{Θ_1}=-Δ_ϕ$, where $Δ_ϕ=(d-2+η)/2$. In the gradient sector, removing the detailed-balance direction leaves two genuinely nonequilibrium modes, chemical and current-like. Two smooth regulators give $y_{Θ_1}\simeq-0.52$, $y_J\simeq-0.56$, and $y_{\rm ch}\simeq-0.89$. A translation Ward identity expresses the current operator as the divergence of the stress tensor. Together with conservation and Itô causality, this forbids chemical operators from generating the current mode, making the nonequilibrium stability matrix triangular; an independent two-loop calculation in $d=4-\varepsilon$ finds no additional current contact counterterm. Within the FRG truncation, $y_J-y_{Θ_1}=-η$; beyond it, this relation requires the absence of an additional contact anomaly. Using the 3D Ising value $η=0.0362978(20)$ [Kos et al., 2016] gives $y_{Θ_1}\simeq-0.5181$ and $y_J\simeq-0.5544$. Because these exponents nearly coincide, single-power fits yield amplitude-dependent apparent exponents and crossover lengths may exceed accessible system sizes. We derive the resulting finite-size scaling rules: odd block observables respond linearly to activity, while even observables receive only quadratic corrections.

cond-mat.stat-mech↗