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arXiv:2012.14436 · SciPost Physics

How many particles make up a chaotic many-body quantum system?

Guy Zisling, Lea Santos, Yevgeny Bar Lev

Published Apr 23, 2021• 20 citations
arXivHTMLPDF

Abstract

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

DOI
10.21468/scipostphys.10.4.088

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We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.
Integrable quantum systems of finite size are generically robust against weak enough integrability-breaking perturbations, but become quantum chaotic and thermalizing if the integrability breaking is strong enough. We argue that the onset of quantum chaos can be described as a Fock-space delocalization process, with the eigenstates of the integrable system being taken as the Fock states. The integrability-breaking perturbation introduces hopping in this Fock space, and chaos sets in when this hopping delocalizes the many-body eigenstates in this space. Depending on the range of the dominant Fock-space hopping, delocalization can occur either through a crossover or via a transition that becomes sharp in the appropriate large-system dynamic limit. In either case, the perturbation strength at the onset of chaos scales to zero in the usual thermodynamic limit, with a size dependence that we estimate analytically and compute numerically for a few specific models. We also identify two intermediate finite-size-dependent regimes: There is generally an intermediate nonchaotic regime in which integrability is broken strongly enough to produce some systemwide many-body resonances but not enough to thermalize the system. In spatially extended systems (but not in quantum dots) there is also a crossover or transition between chaotic regimes where the ratio of the system size to the mean free path of the quasiparticles of the integrable system is small versus large compared to unity.
The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of a system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an improved exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.
The low-energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some sig- natures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. In contrast, they become suppressed when the particle imbalance is increased.
We numerically study quantum chaos properties of long-range XXZ dipolar Hamiltonian spin systems. Two geometries are considered: (i) an open chain with 19 spins, (ii) a face-centered cubic lattice with 14 spins. Energy level-spacing distribution indicates that the three-dimensional geometry is highly chaotic, while the one-dimensional system is mildly chaotic for small chains, but has increasing chaoticity for larger chains. We also look at statistical properties of energy eigenvectors, and of one- and two-body local observables. Finally, we present some preliminary results on time-evolution, local spin dynamics and thermalization. Quantum chaos may have important implications for "scrambling" of quantum information, in both condensed matter systems and in astrophysical applications such as black holes.