1,515 research outputs found
Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study
Using the density-matrix renormalization-group, we investigate the critical
behavior of the anisotropic Heisenberg chains with spins up to . We show
that through the relations arising from the conformal invariance and the DMRG
technique it is possible to obtain accurate finite-size estimates of the
conformal anomaly , the sound velocity , the anomalous dimension
, and the surface exponent of the anisotropic spin-
Heisenberg chains with relatively good accuracy without fitting parameters. Our
results indicate that the entanglement entrop of the spin-
Heisenberg chains satisfies the relation
for in the thermodynamic limit.Comment: 7 pages, 3 figs., 3 tables, to appear in PRB. Added new results for
s>1/
Fermionic field theory for directed percolation in (1+1) dimensions
We formulate directed percolation in (1+1) dimensions in the language of a
reaction-diffusion process with exclusion taking place in one space dimension.
We map the master equation that describes the dynamics of the system onto a
quantum spin chain problem. From there we build an interacting fermionic field
theory of a new type. We study the resulting theory using renormalization group
techniques. This yields numerical estimates for the critical exponents and
provides a new alternative analytic systematic procedure to study
low-dimensional directed percolation.Comment: 20 pages, 2 figure
Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
The momentum distribution in a Fermi gas with two spin states and a large
scattering length has a tail that falls off like 1/k^4 at large momentum k, as
pointed out by Shina Tan. He used novel methods to derive exact relations
between the coefficient of the tail in the momentum distribution and various
other properties of the system. We present simple derivations of these
relations using the operator product expansion for quantum fields. We identify
the coefficient as the integral over space of the expectation value of a local
operator that measures the density of pairs.Comment: 4 pages, 2 figure
Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
A set of universal relations between various properties of any few-body or
many-body system consisting of fermions with two spin states and a large but
finite scattering length have been derived by Shina Tan. We derive
generalizations of the Tan relations for a two-channel model for fermions near
a Feshbach resonance that includes a molecular state whose detuning energy
controls the scattering length. We use quantum field theory methods, including
renormalization and the operator product expansion, to derive these relations.
They reduce to the Tan relations as the scattering length is made increasingly
large.Comment: 25 pages, 8 figure
Reaction-controlled diffusion: Monte Carlo simulations
We study the coupled two-species non-equilibrium reaction-controlled
diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by
means of detailed Monte Carlo simulations in one and two dimensions. Particles
of type A may independently hop to an adjacent lattice site provided it is
occupied by at least one B particle. The B particle species undergoes
diffusion-limited reactions. In an active state with nonzero, essentially
homogeneous B particle saturation density, the A species displays normal
diffusion. In an inactive, absorbing phase with exponentially decaying B
density, the A particles become localized. In situations with algebraic decay
rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous
phase transition separating active and absorbing states, or in a power-law
inactive phase, the A particles propagate subdiffusively with mean-square
displacement ~ t^{1-alpha_A}. We find that within the accuracy of
our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field
approach. This remains true even in the presence of strong spatio-temporal
fluctuations of the B density. However, in contrast with the mean-field
results, our data yield a distinctly non-Gaussian A particle displacement
distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar
for the different processes investigated here. Fluctuations of effective
diffusion rates cause a marked enhancement of n_A(x,t) at low displacements
|x|, indicating a considerable fraction of practically localized A particles,
as well as at large traversed distances.Comment: Revtex, 19 pages, 27 eps figures include
Junctions of anyonic Luttinger wires
We present an extended study of anyonic Luttinger liquids wires jointing at a
single point. The model on the full line is solved with bosonization and the
junction of an arbitrary number of wires is treated imposing boundary
conditions that preserve exact solvability in the bosonic language. This allows
to reach, in the low momentum regime, some of the critical fixed points found
with the electronic boundary conditions. The stability of all the fixed points
is discussed.Comment: 16 pages, 2 figures, typos corrected, Refs adde
Statistics of trajectories in two-state master equations
We derive a simple expression for the probability of trajectories of a master
equation. The expression is particularly useful when the number of states is
small and permits the calculation of observables that can be defined as
functionals of whole trajectories. We illustrate the method with a two-state
master equation, for which we calculate the distribution of the time spent in
one state and the distribution of the number of transitions, each in a given
time interval. These two expressions are obtained analytically in terms of
modified Bessel functions.Comment: 4 pages, 3 figure
Interacting Electrons and Localized Spins: Exact Results from Conformal Field Theory
We give a brief review of the Kondo effect in a one-dimensional interacting
electron system, and present exact results for the impurity thermodynamic
response based on conformal field theory.Comment: 6 pages LaTeX. To appear in the Proceedings of the 1995 Schladming
Winter School on Low-Dimensional Models in Statistical Physics and Quantum
Field Theor
Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models
The finite-size scaling functions for anisotropic three-dimensional Ising
models of size (: anisotropy parameter) are
studied by Monte Carlo simulations. We study the dependence of finite-size
scaling functions of the Binder parameter and the magnetization
distribution function . We have shown that the finite-size scaling
functions for at the critical temperature change from a two-peak
structure to a single-peak one by increasing or decreasing from 1. We also
study the finite-size scaling near the critical temperature of the layered
square-lattice Ising model, when the systems have a large two-dimensional
anisotropy. We have found the three-dimensional and two-dimensional finite-size
scaling behavior depending on the parameter which is fixed; a unified view of
3D and 2D finite-size scaling behavior has been obtained for the anisotropic 3D
Ising models.Comment: 6 pages including 11 eps figures, RevTeX, to appear in J. Phys.
Magnetic exponents of two-dimensional Ising spin glasses
The magnetic critical properties of two-dimensional Ising spin glasses are
controversial. Using exact ground state determination, we extract the
properties of clusters flipped when increasing continuously a uniform field. We
show that these clusters have many holes but otherwise have statistical
properties similar to those of zero-field droplets. A detailed analysis gives
for the magnetization exponent delta = 1.30 +/- 0.02 using lattice sizes up to
80x80; this is compatible with the droplet model prediction delta = 1.282. The
reason for previous disagreements stems from the need to analyze both singular
and analytic contributions in the low-field regime.Comment: 4 pages, 4 figures, title now includes "Ising
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