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

Abstract

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 solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the freemore » energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.« less

Authors:

Jia, Yiyang  ^[1];

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• Search DOE PAGES for ORCID "0000-0001-9006-2990"

Rosa, Dario  ^[2];

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• Search DOE PAGES for ORCID "0000-0001-9747-1033"

Verbaarschot, Jacobus M.  ^[3]

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• Search DOE PAGES for ORCID "0000-0001-5647-6575"

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+ Show Author Affiliations

1. Weizmann Institute of Science, Rehovot (Israel)
2. Institute of Basic Science (IBS), Daejeon (Korea, Republic of)
3. Stony Brook Univ., NY (United States)

Publication Date:

Fri Oct 14 00:00:00 EDT 2022

Research Org.:

Stony Brook Univ., NY (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

2280814

Alternate Identifier(s):

OSTI ID: 1892346

Grant/Contract Number:  

FG02-88ER40388; FAG-88FR40388; IBS-R024-Y2; IBS-R024-D1

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Mathematical Physics

Additional Journal Information:

Journal Volume: 63; Journal Issue: 10; Journal ID: ISSN 0022-2488

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS; phase transitions; many body systems; fermions; Dyson-Schwinger equation; sigma model; statistical thermodynamics