205 research outputs found
Diffusion in higher dimensional SYK model with complex fermions
We construct a new higher dimensional SYK model with complex fermions on
bipartite lattices. As an extension of the original zero-dimensional SYK model,
we focus on the one-dimension case, and similar Hamiltonian can be obtained in
higher dimensions. This model has a conserved U(1) fermion number Q and a
conjugate chemical potential \mu. We evaluate the thermal and charge diffusion
constants via large q expansion at low temperature limit. The results show that
the diffusivity depends on the ratio of free Majorana fermions to Majorana
fermions with SYK interactions. The transport properties and the butterfly
velocity are accordingly calculated at low temperature. The specific heat and
the thermal conductivity are proportional to the temperature. The electrical
resistivity also has a linear temperature dependence term.Comment: 15 pages, 1 figure, add 4 references and fix some typos in this
versio
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
Thickening and sickening the SYK model
We discuss higher dimensional generalizations of the 0+1-dimensional
Sachdev-Ye-Kitaev (SYK) model that has recently become the focus of intensive
interdisciplinary studies by, both, the condensed matter and field-theoretical
communities. Unlike the previous constructions where multiple SYK copies would
be coupled to each other and/or hybridized with itinerant fermions via
spatially short-ranged random hopping processes, we study algebraically varying
long-range (spatially and/or temporally) correlated random couplings in the
general d+1 dimensions. Such pertinent topics as translationally-invariant
strong-coupling solutions, emergent reparametrization symmetry, effective
action for fluctuations, chaotic behavior, and diffusive transport (or a lack
thereof) are all addressed. We find that the most appealing properties of the
original SYK model that suggest the existence of its 1+1-dimensional
holographic gravity dual do not survive the aforementioned generalizations,
thus lending no additional support to the hypothetical broad (including
'non-AdS/non-CFT') holographic correspondence.Comment: Updated and extended version. Latex, no figure
Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation
We show that there exists a class of charged BTZ-like black hole solutions in
Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is
characterized by a charge-dependent logarithmic term in the metric function. As
concrete examples, we give five such charged BTZ-like black hole solutions and
the standard charged BTZ metric can be regarded as a special instance of them.
In order to check the recent proposed universal relations between diffusivity
and the butterfly velocity, we first compute the diffusion constants of the
standard charged BTZ black holes and then extend our calculation to arbitrary
dimension , exponents and . Remarkably, the case and
is a very special in that the charge diffusion is a constant and
the energy diffusion might be ill-defined, but diverges. We
also compute the diffusion constants for the case that the DC conductivity is
finite but in the absence of momentum relaxation.Comment: 30 pages, 2 figure
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
SYK Model, Chaos and Conserved Charge
We study the SYK model with complex fermions, in the presence of an
all-to-all -body interaction, with a non-vanishing chemical potential. We
find that, in the large limit, this model can be solved exactly and the
corresponding Lyapunov exponent can be obtained semi-analytically. The
resulting Lyapunov exponent is a sensitive function of the chemical potential
. Even when the coupling , which corresponds to the disorder averaged
values of the all to all fermion interaction, is large, values of which
are exponentially small compared to lead to suppression of the Lyapunov
exponent.Comment: 18pages, 4 figures, v2:references and acknowledgment added, typos
correcte
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