9,813 research outputs found
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
The Sachdev-Ye-Kitaev model is a -dimensional model describing
Majorana fermions or complex fermions with random interactions. This model has
various interesting properties such as approximate local criticality (power law
correlation in time), zero temperature entropy, and quantum chaos. In this
article, we propose a higher dimensional generalization of the
Sachdev-Ye-Kitaev model, which is a lattice model with Majorana fermions at
each site and random interactions between them. Our model can be defined on
arbitrary lattices in arbitrary spatial dimensions. In the large limit, the
higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev
model such as local criticality in two-point functions, zero temperature
entropy and chaos measured by the out-of-time-ordered correlation functions. In
addition, we obtain new properties unique to higher dimensions such as
diffusive energy transport and a "butterfly velocity" describing the
propagation of chaos in space. We mainly present results for a
-dimensional example, and discuss the general case near the end.Comment: 1+37 pages, published versio
Spread of entanglement in a Sachdev-Ye-Kitaev chain
We study the spread of R\'enyi entropy between two halves of a
Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield
double (TFD) state. The SYK chain model is a model of chaotic many-body
systems, which describes a one-dimensional lattice of Majorana fermions, with
spatially local random quartic interaction. We find that for integer R\'enyi
index , the R\'enyi entanglement entropy saturates at a parametrically
smaller value than expected. This implies that the TFD state of the SYK chain
does not rapidly thermalize, despite being maximally chaotic: instead, it
rapidly approaches a prethermal state. We compare our results to the signatures
of thermalization observed in other quenches in the SYK model, and to intuition
from nearly- gravity.Comment: 1+46 pages, 11 figure
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