arXiv:1902.09970 · Journal of High Energy Physics

Spontaneous symmetry breaking in fermionic random matrix model

I. Ya. Aref’eva, Igor Volovich

Published Oct 1, 2019• 11 citations

Abstract

Abstract A fermionic random matrix model, which is a 0-dimensional version of the SYK model with replicas, is considered. The replica-off-diagonal correlation functions vanish at finite N, but we show that they do not vanish in the large N limit due to spontaneous symmetry breaking. We use the Bogoliubov quasi-averages approach to studying phase transitions. The consideration may be relevant to the study of the problem of existence of the spin glass phase in fermionic models.

DOI: 10.1007/jhep10(2019)114

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arXiv:1902.09970 · Journal of High Energy Physics

Spontaneous symmetry breaking in fermionic random matrix model

I. Ya. Aref’eva, Igor Volovich

Published Oct 1, 2019• 11 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep10(2019)114

Related papers

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Abstract We investigate the nonperturbative effects in the Sadchev–Ye–Kitaev (SYK) model at large

N

. The replica-nondiagonal solutions are considered in the SYK model with an integer number of replicas

M > 1

. An important property of such solutions is the fact that they realize spontaneous breaking of the time translation group on

M

replicas of the thermal circle. It is demonstrated in this study that this spontaneous symmetry breaking can be described in terms of the Bogolyubov quasi-averages, if we consider the system of nonlocally interacting replicas of the SYK model. The inclusion of the interaction of the replicas in this system transforms the subleading replica-nondiagonal saddle points from a pure SYK to thermodynamic phases, thereby generating a nontrivial phase structure. We investigate this phase structure exactly analytically in the SYK2 model and numerically in the SYK4 model.

We analyze the infinite range Ising spin glass in a transverse-field $\ensuremath{\Gamma}$ below the critical temperature by a one step replica symmetry breaking theory. The set of

n

replicas is divided in

r

blocks of

m

replicas each. We present results for different values of the block-size parameter

m

. The spin operators are represented by bilinear combinations of fermionic fields and we compare the results of two models: In the four-states (4-S) model the diagonal

{S}_{i}^{z}

operator has two unphysical vanishing eigenvalues, that are suppressed by a restraint in the two-states (2-S) model. In the static approximation we obtain qualitatively similar results for both models. They both exhibit a critical temperature ${T}_{c}(\ensuremath{\Gamma})$ that decreases when $\ensuremath{\Gamma}$ increases, until it reaches a quantum critical point at the same value of ${\ensuremath{\Gamma}}_{c}$ and they are both unstable under replica symmetry breaking in the whole spin glass phase. Below the critical temperature we present results for the order parameters and free energy.