arXiv subjects

Lea F. Santos

Publications and source records attributed to Lea F. Santos.

At least 73 records · Page 4Linked to original sources

arXiv2021

Speck of Chaos

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

cond-mat.stat-mech↗

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↗

arXiv2020

Experimental Detection of the Correlation Rényi Entropy in the Central Spin Model

We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with 15 other spins. Due to the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multi-spin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multi-spin correlations and use them to compute the evolution of what we call correlation Rényi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation Rényi entropy depend on the system size.

quant-ph↗

arXiv2020

Sensitivity of quantum information to environment perturbations measured with a non-local out-of-time-order correlation function

In a quantum system coupled with a non-Markovian environment, quantum information may flow out of or in to the system. Measuring quantum information flow and its sensitivity to perturbations is important for a better understanding of open quantum systems and for the implementation of quantum technologies. Information gets shared between a quantum system and its environment by means of system-environment correlations (SECs) that grow during their interaction. We design a nuclear magnetic resonance (NMR) experiment to directly observe the evolution of the SECs and use the second moment of their distribution as a natural metric for quantifying the flow of information. In a second experiment, by accounting for the environment dynamics, we study the sensitivity of the shared quantum information to perturbations in the environment. The metric used in this case is a non-local out-of-time-order correlation function (OTOC). By analyzing the decay of the OTOC as a function of the SEC spread, instead of the evolution time, we are able to demonstrate its exponential behavior.

quant-ph↗

arXiv2020

Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present work addresses what happens out of equilibrium, as the increase of the strength of onsite disorder takes the system to the localized phase. We consider two local and two non-local quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the time scale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times, while the non-local quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis are provided using the $\ell$-bits model and a toy model.

cond-mat.stat-mech↗

arXiv2020

Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.

cond-mat.stat-mech↗

arXiv2020

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.

cond-mat.stat-mech↗

arXiv2020

Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman.

cond-mat.dis-nn↗

arXiv2019

Calculation of Transition State Energies in the HCN-HNC Isomerization with an Algebraic Model

Recent works have shown that the spectroscopic access to highly-excited states provides enough information to characterize transition states in isomerization reactions. Here, we show that the transition state of the bond breaking HCN-HNC isomerization reaction can also be achieved with the two-dimensional limit of the algebraic vibron model. We describe the system's bending vibration with the algebraic Hamiltonian and use its classical limit to characterize the transition state. Using either the coherent state formalism or a recently proposed approach by Baraban et al. [ Science 2015 , 350 , 1338], we obtain an accurate description of the isomerization transition state. In addition, we show that the energy level dynamics and the transition state wave function structure indicate that the spectrum in the vicinity of the isomerization saddle point can be understood in terms of the formalism for excited state quantum phase transitions.

physics.chem-ph↗

arXiv2019

Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model

This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal onsite disorder strength $W$. But this is not the case when the model is finite and the localization length is larger than the system size $L$, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter $ξ\propto (W^2 L)^{-1}$. As $ξ$ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster that when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for $W=0$, when it is in fact deeper.

cond-mat.dis-nn↗

arXiv2019

Thouless and relaxation time scales in many-body quantum systems

A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time scales can be analytically found by analyzing dynamical manifestations of spectral correlations. Using this approach, we show that the Thouless time, $t_{\text{Th}}$, and the relaxation time, $t_{\text{R}}$, increase exponentially with system size. We define $t_{\text{Th}}$ as the time at which the spread of the initial state in the many-body Hilbert space is complete and verify that it agrees with the inverse of the Thouless energy. $t_{\text{Th}}$ marks the point beyond which the dynamics acquire universal features, while relaxation happens later when the evolution reaches a stationary state. In chaotic systems, $t_{\text{Th}}\ll t_{\text{R}}$, while for systems approaching a many-body localized phase, $t_{\text{Th}}\rightarrow t_{\text{R}}$. Our analytical results for $t_{\text{Th}}$ and $t_{\text{R}}$ are obtained for the survival probability, which is a global quantity. We show numerically that the same time scales appear also in the evolution of the spin autocorrelation function, which is an experimental local observable. Our studies are carried out for realistic many-body quantum models. The results are compared with those for random matrices.

cond-mat.stat-mech↗

arXiv2019

Exponentially fast dynamics of chaotic many-body systems

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width $Γ$ of the local density of states (LDOS) and is associated with the Kolmogorov-Sinai entropy for systems with a well defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the saturation and show that it is much larger than $\hbar/Γ$. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.

cond-mat.stat-mech↗

arXiv2019

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.

cond-mat.stat-mech↗

arXiv2019

Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator

We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-$1/2$. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components $N_{pc}$ (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev. E 99, 010101R (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time-dependence. We show that $N_{pc}$ can be formally expressed as the inverse of the sum of all OTOC's for projection operators. While none of the individual projection-OTOC's shows an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the $N_{pc}$ helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.

cond-mat.stat-mech↗

arXiv2019

Analytical description of the survival probability of coherent states in regular regimes

Using coherent states as initial states, we investigate the quantum dynamics of the Lipkin-Meshkov-Glick (LMG) and Dicke models in the semi-classical limit. They are representative models of bounded systems with one- and two-degrees of freedom, respectively. The first model is integrable, while the second one has both regular and chaotic regimes. Our analysis is based on the survival probability. Within the regular regime, the energy distribution of the initial coherent states consists of quasi-harmonic sub-sequences of energies with Gaussian weights. This allows for the derivation of analytical expressions that accurately describe the entire evolution of the survival probability, from $t=0$ to the saturation of the dynamics. The evolution shows decaying oscillations with a rate that depends on the anharmonicity of the spectrum and, in the case of the Dicke model, on interference terms coming from the simultaneous excitation of its two-degrees of freedom. As we move away from the regular regime, the complexity of the survival probability is shown to be closely connected with the properties of the corresponding classical phase space. Our approach has broad applicability, since its central assumptions are not particular of the studied models.

quant-ph↗

arXiv2018

From few- to many-body quantum systems

How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that convergence for the static properties of the system with few particles to the many-body limit is fast. For $N \gsim 4$, the density of states is already very close to Gaussian and signatures of many-body quantum chaos, such as level repulsion and fully extended eigenstates, become evident. The dynamics, on the other hand, depend on the initial state and time scale. In dilute systems, as the particles move away from each other, the entropy growth changes in time from linear, as typical for many-body systems, to logarithmic.

cond-mat.stat-mech↗

arXiv2018

Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"

In a recent Letter [PhysRevLett.119.030601 (2017), arXiv:1702.08227], Shiraishi and Mori claim to provide a general method for constructing local Hamiltonians that do not exhibit eigenstate thermalization. We argue that the claim is based on a misunderstanding of the eigenstate thermalization hypothesis (ETH). More specifically, on the assumption that ETH is valid for the entire Hamiltonian matrix instead of each symmetry sector independently. We discuss what happens if one mixes symmetry sectors in the two-dimensional transverse field Ising model.

cond-mat.stat-mech↗

arXiv2018

Relaxation, chaos, and thermalization in a three-mode model of a BEC

We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose-Einstein condensed state, well described by Thomas-Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.

cond-mat.quant-gas↗