# Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

@article{Jia2022ReplicaSB, title={Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model}, author={Yiyang Jia and Dario Rosa and Jacobus J. M. Verbaarschot}, journal={Journal of Mathematical Physics}, year={2022} }

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by…

## One Citation

### Binary-coupling sparse SYK: an improved model of quantum chaos and holography

- Computer Science, Physics
- 2022

The binary-coupling sparse SYK model, which is better suited for analog or digital quantum simulations of quantum chaotic behavior and holographic metals due to its simplicity and scaling properties, is proposed.

## References

SHOWING 1-10 OF 83 REFERENCES

### On the replica structure of Sachdev-Ye-Kitaev model

- PhysicsJournal of High Energy Physics
- 2019

We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation…

### Euclidean wormhole in the Sachdev-Ye-Kitaev model

- Physics
- 2021

We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify a low temperature transition to a gapped phase characterized by a constant in temperature free energy. This…

### Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation

- Physics, Mathematics
- 2004

### Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.

- PhysicsPhysical review letters
- 2018

Analytically and numerically it is shown that a generalized SYK model with an additional one-body infinite-range random interaction is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature.

### Replica-nondiagonal solutions in the SYK model

- MathematicsJournal of High Energy Physics
- 2019

We study the SYK model in the large N limit beyond the replica-diagonal approximation. First we show that there are exact replica-nondiagonal solutions of the saddle point equations for q = 2 for any…

### Structure of Lefschetz thimbles in simple fermionic systems

- Physics
- 2014

A bstractThe Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach…

### From operator statistics to wormholes

- MathematicsPhysical Review Research
- 2021

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding…

### Lindbladian dissipation of strongly-correlated quantum matter

- PhysicsPhysical Review Research
- 2022

We propose the Sachdev-Ye-Kitaev Lindbladian as a paradigmatic solvable model of dissipative many-body quantum chaos. It describes N strongly coupled Majorana fermions with random all-to-all…