647 research outputs found
Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
By relating the ground state of Temperley-Lieb hamiltonians to partition
functions of 2D statistical mechanics systems on a half plane, and using a
boundary Coulomb gas formalism, we obtain in closed form the valence bond
entanglement entropy as well as the valence bond probability distribution in
these ground states. We find in particular that for the XXX spin chain, the
number N_c of valence bonds connecting a subsystem of size L to the outside
goes, in the thermodynamic limit, as = (4/pi^2) ln L, disproving a recent
conjecture that this should be related with the von Neumann entropy, and thus
equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.Comment: 4 pages, 2 figure
A constrained Potts antiferromagnet model with an interface representation
We define a four-state Potts model ensemble on the square lattice, with the
constraints that neighboring spins must have different values, and that no
plaquette may contain all four states. The spin configurations may be mapped
into those of a 2-dimensional interface in a 2+5 dimensional space. If this
interface is in a Gaussian rough phase (as is the case for most other models
with such a mapping), then the spin correlations are critical and their
exponents can be related to the stiffness governing the interface fluctuations.
Results of our Monte Carlo simulations show height fluctuations with an
anomalous dependence on wavevector, intermediate between the behaviors expected
in a rough phase and in a smooth phase; we argue that the smooth phase (which
would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.
Corner transfer matrix renormalization group method for two-dimensional self-avoiding walks and other O(n) models
We present an extension of the corner transfer matrix renormalisation group
(CTMRG) method to O(n) invariant models, with particular interest in the
self-avoiding walk class of models (O(n=0)). The method is illustrated using an
interacting self-avoiding walk model. Based on the efficiency and versatility
when compared to other available numerical methods, we present CTMRG as the
method of choice for two-dimensional self-avoiding walk problems.Comment: 4 pages 7 figures Substantial rewrite of previous version to include
calculations of critical points and exponents. Final version accepted for
publication in PRE (Rapid Communications
Critical points in coupled Potts models and critical phases in coupled loop models
We show how to couple two critical Q-state Potts models to yield a new
self-dual critical point. We also present strong evidence of a dense critical
phase near this critical point when the Potts models are defined in their
completely packed loop representations. In the continuum limit, the new
critical point is described by an SU(2) coset conformal field theory, while in
this limit of the the critical phase, the two loop models decouple. Using a
combination of exact results and numerics, we also obtain the phase diagram in
the presence of vacancies. We generalize these results to coupling two Potts
models at different Q.Comment: 23 pages, 10 figure
Critical exponents of domain walls in the two-dimensional Potts model
We address the geometrical critical behavior of the two-dimensional Q-state
Potts model in terms of the spin clusters (i.e., connected domains where the
spin takes a constant value). These clusters are different from the usual
Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross
and branch. We develop a transfer matrix technique enabling the formulation and
numerical study of spin clusters even when Q is not an integer. We further
identify geometrically the crossing events which give rise to conformal
correlation functions. This leads to an infinite series of fundamental critical
exponents h_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the
insertion of l_1 thin and l_2 thick domain walls.Comment: 5 pages, 3 figures, 1 tabl
Exact critical points of the O() loop model on the martini and the 3-12 lattices
We derive the exact critical line of the O() loop model on the martini
lattice as a function of the loop weight .A finite-size scaling analysis
based on transfer matrix calculations is also performed.The numerical results
coincide with the theoretical predictions with an accuracy up to 9 decimal
places. In the limit , this gives the exact connective constant
of self-avoiding walks on the martini lattice. Using
similar numerical methods, we also study the O() loop model on the 3-12
lattice. We obtain similarly precise agreement with the exact critical points
given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].Comment: 4 pages, 3 figures, 2 table
An Intersecting Loop Model as a Solvable Super Spin Chain
In this paper we investigate an integrable loop model and its connection with
a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some
properties of the ground state. When the loop fugacity lies in the physical
regime, we conjecture that the central charge is for integer .
Low-lying excitations are examined, supporting a superdiffusive behavior for
. We argue that these systems are interesting examples of integrable
lattice models realizing conformal field theories.Comment: latex file, 7 page
Entanglement in gapless resonating valence bond states
We study resonating-valence-bond (RVB) states on the square lattice of spins
and of dimers, as well as SU(N)-invariant states that interpolate between the
two. These states are ground states of gapless models, although the
SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its
spinful sector. We show that the gapless behavior in spin and dimer RVB states
is qualitatively similar by studying the R\'enyi entropy for splitting a torus
into two cylinders, We compute this exactly for dimers, showing it behaves
similarly to the familiar one-dimensional log term, although not identically.
We extend the exact computation to an effective theory believed to interpolate
among these states. By numerical calculations for the SU(2) RVB state and its
SU(N)-invariant generalizations, we provide further support for this belief. We
also show how the entanglement entropy behaves qualitatively differently for
different values of the R\'enyi index , with large values of proving a
more sensitive probe here, by virtue of exhibiting a striking even/odd effect.Comment: 44 pages, 14 figures, published versio
Entanglement entropy of two disjoint intervals in conformal field theory
We study the entanglement of two disjoint intervals in the conformal field
theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any
integer n is calculated as the four-point function of a particular type of
twist fields and the final result is expressed in a compact form in terms of
the Riemann-Siegel theta functions. In the decompactification limit we provide
the analytic continuation valid for all model parameters and from this we
extract the entanglement entropy. These predictions are checked against
existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos
corrected and refs adde
The "topological" charge for the finite XX quantum chain
It is shown that an operator (in general non-local) commutes with the
Hamiltonian describing the finite XX quantum chain with certain non-diagonal
boundary terms. In the infinite volume limit this operator gives the
"topological" charge.Comment: 5 page
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