arXiv subjects

Marco Távora

Publications and source records attributed to Marco Távora.

6 recordsLinked to original sources

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↗

arXiv2017

Power-law decay exponents: a dynamical criterion for predicting thermalization

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior $\propto t^{-γ}$ of the survival probability at long times. We show that the value of the power-law exponent $γ$ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in details: $γ\ge 2$ and $γ<1$. Exponents $γ\ge 2$ imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with $γ< 1$ emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

cond-mat.stat-mech↗

arXiv2016

Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization

Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior $\propto t^{ - γ}$. This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of $γ$. From it, we can anticipate whether the initial state will or will not thermalize.

cond-mat.stat-mech↗

arXiv2016

Realistic many-body quantum systems vs full random matrices: static and dynamical properties

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.

cond-mat.stat-mech↗

arXiv2016

Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation

Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.

cond-mat.stat-mech↗

arXiv2016

Survival Probability of the Néel State in Clean and Disordered Systems: an Overview

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the Néel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.

cond-mat.dis-nn↗