Kavli Affiliate: Cheng Peng
| First 5 Authors: Ping Gao, Han Lin, Cheng Peng, ,
| Summary:
We construct a new family of quantum chaotic models by combining multiple
copies of integrable commuting SYK models. As each copy of the commuting SYK
model does not commute with others, this construction breaks the integrability
of each commuting SYK and the family of models demonstrates the emergence of
quantum chaos. We study the spectrum of this model analytically in the
double-scaled limit. As the number of copies tends to infinity, the spectrum
becomes compact and equivalent to the regular SYK model. For finite $d$ copies,
the spectrum is close to the regular SYK model in UV but has an exponential
tail $e^{E/T_c}$ in the IR. We identify the reciprocal of the exponent in the
tail as a critical temperature $T_c$, above which the model should be quantum
chaotic. $T_c$ monotonically decreases as $d$ increases, which expands the
chaotic regime over the non-chaotic regime. We propose the existence of a new
phase around $T_c$, and the dynamics should be very different in two phases. We
further carry out numeric analysis at finite $d$, which supports our proposal.
Given any finite dimensional local Hamiltonian, by decomposing it into $d$
groups, in which all terms in one group commute with each other but terms from
different groups may not, our analysis can give an estimate of the critical
temperature for quantum chaos based on the decomposition. We also comment on
the implication of the critical temperature to future quantum simulations of
quantum chaos and quantum gravity.
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