Speck of chaos

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.

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“…The fact that the addition of a defect takes the system to the chaotic regime was demonstrated in Refs. [36][37][38][39].…”

Section: Integrable and Chaotic Pointsmentioning

confidence: 99%

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

2021

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“…They can be done over initial states, disorder realizations, or, as in our case, they correspond to moving time averages. The correlation hole detects short-and long-range correlations in the spectrum, and in addition, it does not require unfolding the spectrum or separating it by symmetries [29,92]. In cold atom systems the survival probability is commonly used to probe the non-equilibrium dynamics of few- [23,62] and many-body systems [26,35,42,63], and can be experimentally measured using interferometric techniques [24].…”

Section: Survival Probabilitymentioning

confidence: 99%

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Fogarty

García-March

Santos

et al. 2021

Quantum

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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.

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“…Much of the research on the phenomenon of many-body localization has been carried out with the Heisenberg XXZ spin chain [16][17][18][19][20][21][22][23][24][25][26][27][28]52], which takes into account nearest-neighbors interactions only. In comparison, its simplest generalization, the J 1 -J 2 model, has been somewhat less explored.…”

Section: Model: the Disordered J 1 -J Chain And Many-body Localizationmentioning

confidence: 99%

Signatures of a critical point in the many-body localization transition

2021

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Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

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Speck of chaos

Cited by 50 publications

References 81 publications

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

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

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Signatures of a critical point in the many-body localization transition

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