14,529 research outputs found
Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
We investigate a weak version of subsystem eigenstate thermalization
hypothesis (ETH) for a two-dimensional large central charge conformal field
theory by comparing the local equivalence of high energy state and thermal
state of canonical ensemble. We evaluate the single-interval R\'enyi entropy
and entanglement entropy for a heavy primary state in short interval expansion.
We verify the results of R\'enyi entropy by two different replica methods. We
find nontrivial results at the eighth order of short interval expansion, which
include an infinite number of higher order terms in the large central charge
expansion. We then evaluate the relative entropy of the reduced density
matrices to measure the difference between the heavy primary state and thermal
state of canonical ensemble, and find that the aforementioned nontrivial eighth
order results make the relative entropy unsuppressed in the large central
charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can
exploit the results of relative entropy to yield the lower and upper bounds on
trace distance of the excited-state and thermal-state reduced density matrices.
Our results are consistent with subsystem weak ETH, which requires the above
trace distance is of power-law suppression by the large central charge.
However, we are unable to pin down the exponent of power-law suppression. As a
byproduct we also calculate the relative entropy to measure the difference
between the reduced density matrices of two different heavy primary states.Comment: 28 pages, 4 figures;v2 change author list;v3 related subtleties about
weak ETH clarified; v4 minor correction to match JHEP versio
Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
We calculate various quantities that characterize the dissimilarity of
reduced density matrices for a short interval of length in a
two-dimensional (2D) large central charge conformal field theory (CFT). These
quantities include the R\'enyi entropy, entanglement entropy, relative entropy,
Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt
the method of operator product expansion of twist operators, and calculate the
short interval expansion of these quantities up to order of for the
contributions from the vacuum conformal family. The formal forms of these
dissimilarity measures and the derived Fisher information metric from
contributions of general operators are also given. As an application of the
results, we use these dissimilarity measures to compare the excited and thermal
states, and examine the eigenstate thermalization hypothesis (ETH) by showing
how they behave in high temperature limit. This would help to understand how
ETH in 2D CFT can be defined more precisely. We discuss the possibility that
all the dissimilarity measures considered here vanish when comparing the
reduced density matrices of an excited state and a generalized Gibbs ensemble
thermal state. We also discuss ETH for a microcanonical ensemble thermal state
in a 2D large central charge CFT, and find that it is approximately satisfied
for a small subsystem and violated for a large subsystem.Comment: V1, 34 pages, 5 figures, see collection of complete results in the
attached Mathematica notebook; V2, 38 pages, 5 figures, published versio
Unified tensor network theory for frustrated classical spin models in two dimensions
Frustration is a ubiquitous phenomenon in many-body physics that influences
the nature of the system in a profound way with exotic emergent behavior.
Despite its long research history, the analytical or numerical investigations
on frustrated spin models remain a formidable challenge due to their extensive
ground state degeneracy. In this work, we propose a unified tensor network
theory to numerically solve the frustrated classical spin models on various
two-dimensional (2D) lattice geometry with high efficiency. We show that the
appropriate encoding of emergent degrees of freedom in each local tensor is of
crucial importance in the construction of the infinite tensor network
representation of the partition function. The frustrations are thus relieved
through the effective interactions between emergent local degrees of freedom.
Then the partition function is written as a product of a one-dimensional (1D)
transfer operator, whose eigen-equation can be solved by the standard algorithm
of matrix product states rigorously, and various phase transitions can be
accurately determined from the singularities of the entanglement entropy of the
1D quantum correspondence. We demonstrated the power of our unified theory by
numerically solving 2D fully frustrated XY spin models on the kagome, square
and triangular lattices, giving rise to a variety of thermal phase transitions
from infinite-order Brezinskii-Kosterlitz-Thouless transitions, second-order
transitions, to first-order phase transitions. Our approach holds the potential
application to other types of frustrated classical systems like Heisenberg spin
antiferromagnets.Comment: 20 pages, 19 figure
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