Onset of many-body quantum chaos due to breaking integrability
- URL: http://arxiv.org/abs/2112.14762v3
- Date: Mon, 9 May 2022 12:36:34 GMT
- Title: Onset of many-body quantum chaos due to breaking integrability
- Authors: Vir B. Bulchandani, David A. Huse, Sarang Gopalakrishnan
- Abstract summary: We argue that the onset of quantum chaos can be described as a Fock-space delocalization process.
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.
In either case, the perturbation strength at the onset of chaos scales to zero in the usual thermodynamic limit.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 system-wide 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.
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