arXiv subjects

Isaías Vallejo-Fabila

Publications and source records attributed to Isaías Vallejo-Fabila.

7 recordsLinked to original sources

arXiv2026

Probe Signatures of Quantum Chaos with Quantum Sensing

The spectral form factor (SFF), which is the Fourier transform of the two-point spectral correlation, is a fundamental diagnostics of quantum chaos. Nevertheless, its experimental detection in quantum many-body systems was less unexplored until recently. Here, we establish a relationship between the SFF with the quantum Fisher information (QFI) by means of quantum sensing protocols. Furthermore, when the eigenvalues and eigenstates of the disordered Hamiltonian are statistically independent, we prove that QFI is typical both in short and long timescales while numerics suggest that it is also typical at intermediate timescales, which ensures self-averaging of QFI. The self-averaging property renders the experimental measurement of QFI with our protocol less noisy in contrast with the direct measurement of SFF which is known to be non-self-averaging. Our results reveal an intriguing connection between quantum noise and the signatures of quantum chaos.

quant-ph↗

arXiv2026

Thermalization in the mixed-field Ising model: An occupation number perspective

The occupation number is a key observable for diagnosing thermalization, as it connects directly to standard statistical laws such as Fermi--Dirac, Bose--Einstein, and Boltzmann distributions. In the context of spin systems, it represents the population of the sublevels of the magnetization in the $z$-direction. We use this quantity to probe the onset of thermalization in the isolated quantum and classical one-dimensional spin-1 Ising model with transverse and longitudinal fields. Thermalization is achieved when the long-time average of the occupation number converges to the microcanonical prediction as the chain length $L$ increases, consistent with the emergence of ergodicity. However, the finite-size scaling analysis in the quantum model is challenged by the exponential growth of the Hilbert space with $L$. To overcome this limitation, we turn to the corresponding classical model, which enables access to much larger system sizes. By tracking the dynamics of individual spins on their three-dimensional Bloch spheres and employing tools from random matrix theory, we establish a quantitative criterion for classical ergodicity in interacting spin systems. We find that deviations from classical ergodicity decay algebraically with system size. This power-law scaling then provides a quantitative bound on the approach to thermal equilibrium in the quantum model.

cond-mat.stat-mech↗

arXiv2025

Dynamical detection of extended nonergodic states in many-body quantum systems

Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the analysis to relatively small system sizes. In this work, we demonstrate that the correlation fractal dimension $D_2$ can be directly obtained from the long-time dynamics of interacting many-body quantum systems. Specifically, we show that it coincides with the exponent of the power-law decay of the time-averaged survival probability, defined as the fidelity between an initial state and its time-evolved counterpart. This dynamical approach avoids the need for scaling procedures and enables access to larger systems than those typically reachable via exact diagonalization. We test the method on various random matrix ensembles, including full random matrices, the Rosenzweig-Porter model, and power-law banded random matrices, and extend the analysis to interacting many-body systems described by the one-dimensional Aubry-André model and the disordered spin-1/2 Heisenberg chain. In the case of full random matrices, we also derive an analytical expression for the entire evolution of the time-averaged survival probability.

cond-mat.dis-nn↗

arXiv2025

Proposal for many-body quantum chaos detection with single-site measurements

We demonstrate that the long-time dynamics of an observable associated with a single lattice site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, a widely used diagnostic of quantum chaos. In particular, we focus on the partial survival probability and spin autocorrelation function at a single site, both evolved under a disordered spin-1/2 chain, which is a setup realizable in current experimental platforms. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos is feasible, but constrained to small system sizes.

cond-mat.stat-mech↗

arXiv2025

Timescales for thermalization, quantum chaos, and self-averaging

This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process, exhibit dynamical manifestations of spectral correlations as in random matrix theory and investigate how these manifestations affect their equilibration times. We refer to systems presenting these spectral correlations as chaotic quantum systems, although the correct term to be employed, whether chaotic or ergodic quantum systems, is debatable and both have limitations.

cond-mat.stat-mech↗

arXiv2023

Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition

The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of auto-correlated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in time domain, on which we put main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin auto-correlation function.

cond-mat.dis-nn↗

arXiv2021

Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions

In a disordered system, a quantity is self-averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases. Here, we consider a chaotic disordered many-body quantum system and search for a relationship between self-averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales. An exponential distribution, as found for the survival probability at long times, explains its lack of self-averaging, since the mean and the dispersion are equal. Gaussian distributions, however, are obtained for both self-averaging and non-self-averaging quantities. Our studies show also that one can make conclusions about the self-averaging behavior of one quantity based on the distribution of another related quantity. This strategy allows for semianalytical results, and thus circumvents the limitations of numerical scaling analysis, which are restricted to few system sizes.

cond-mat.stat-mech↗