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.

Physics of Particles and NucleiJul 1, 20200 citations

Bulletin of the American Physical Society

Spontaneous Breaking of U(1) Symmetry in Coupled Complex Sachdev-Ye-Kitaev Models

Igor R. Klebanov, Alexey Milekhin, Grigory Tarnopolsky, Wenli Zhao

Published Mar 18, 2021• 0 citations

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Mikhail Alexandrovich Khramtsov

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.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.

Physics of Particles and NucleiJul 1, 20200 citations

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi-liquid phase described by the ordinary

q=4

SYK model has marginally relevant or irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the

{\mathrm{SYK}}_{q}

model with a

q

-fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.

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.