805 research outputs found
The fermion bag approach to lattice field theories
We propose a new approach to the fermion sign problem in systems where there
is a coupling such that when it is infinite the fermions are paired into
bosons and there is no fermion permutation sign to worry about. We argue that
as becomes finite fermions are liberated but are naturally confined to
regions which we refer to as {\em fermion bags}. The fermion sign problem is
then confined to these bags and may be solved using the determinantal trick. In
the parameter regime where the fermion bags are small and their typical size
does not grow with the system size, construction of Monte Carlo methods that
are far more efficient than conventional algorithms should be possible. In the
region where the fermion bags grow with system size, the fermion bag approach
continues to provide an alternative approach to the problem but may lose its
main advantage in terms of efficiency. The fermion bag approach also provides
new insights and solutions to sign problems. A natural solution to the "silver
blaze problem" also emerges. Using the three dimensional massless lattice
Thirring model as an example we introduce the fermion bag approach and
demonstrate some of these features. We compute the critical exponents at the
quantum phase transition and find and .Comment: 31 pages, 9 figures, 5 table
Solution of the Complex Action Problem in the Potts Model for Dense QCD
Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential
suffer from the notorious complex action problem. We consider QCD with
static quarks coupled to a large chemical potential. This leaves us with an
SU(3) Yang-Mills theory with a complex action containing the Polyakov loop.
Close to the deconfinement phase transition the qualitative features of this
theory, in particular its Z(3) symmetry properties, are captured by the 3-d
3-state Potts model. We solve the complex action problem in the Potts model by
using a cluster algorithm. The improved estimator for the -dependent part
of the Boltzmann factor is real and positive and is used for importance
sampling. We localize the critical endpoint of the first order deconfinement
phase transition line and find consistency with universal 3-d Ising behavior.
We also calculate the static quark-quark, quark-anti-quark, and
anti-quark-anti-quark potentials which show screening as expected for a system
with non-zero baryon density.Comment: 28 pages, 7 figure
From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
The numerical simulation of various field theories at non-zero chemical
potential suffers from severe complex action problems. In particular, QCD at
non-zero quark density can presently not be simulated for that reason. A
similar complex action problem arises in the 2-d O(3) model -- a toy model for
QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional
reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The
complex action problem of the 2-d O(3) model manifests itself as a sign problem
of the ladder system. This sign problem is solved completely with a
meron-cluster algorithm.Comment: Based on a talk by U.-J. Wiese, 6 pages, 12 figures, to be published
in computer physics communication
Meron-Cluster Approach to Systems of Strongly Correlated Electrons
Numerical simulations of strongly correlated electron systems suffer from the
notorious fermion sign problem which has prevented progress in understanding if
systems like the Hubbard model display high-temperature superconductivity. Here
we show how the fermion sign problem can be solved completely with
meron-cluster methods in a large class of models of strongly correlated
electron systems, some of which are in the extended Hubbard model family and
show s-wave superconductivity. In these models we also find that on-site
repulsion can even coexist with a weak chemical potential without introducing
sign problems. We argue that since these models can be simulated efficiently
using cluster algorithms they are ideal for studying many of the interesting
phenomena in strongly correlated electron systems.Comment: 36 Pages, 13 figures, plain Late
Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model
The recently developed Meron-Cluster algorithm completely solves the
exponentially difficult sign problem for a number of models previously
inaccessible to numerical simulation. We use this algorithm in a high-precision
study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a
four-fermion interaction. This model cannot be explored using standard
algorithms. We find that the Z(2) chiral symmetry of this model is
spontaneously broken at low temperatures and that the finite-temperature chiral
phase transition is in the universality class of the 2-d Ising model, as
expected.Comment: 18 pages, LaTe
An Introduction to Chiral Symmetry on the Lattice
The chiral symmetry of QCD is of central
importance for the nonperturbative low-energy dynamics of light quarks and
gluons. Lattice field theory provides a theoretical framework in which these
dynamics can be studied from first principles. The implementation of chiral
symmetry on the lattice is a nontrivial issue. In particular, local lattice
fermion actions with the chiral symmetry of the continuum theory suffer from
the fermion doubling problem. The Ginsparg-Wilson relation implies L\"uscher's
lattice variant of chiral symmetry which agrees with the usual one in the
continuum limit. Local lattice fermion actions that obey the Ginsparg-Wilson
relation have an exact chiral symmetry, the correct axial anomaly, they obey a
lattice version of the Atiyah-Singer index theorem, and still they do not
suffer from the notorious doubling problem. The Ginsparg-Wilson relation is
satisfied exactly by Neuberger's overlap fermions which are a limit of Kaplan's
domain wall fermions, as well as by Hasenfratz and Niedermayer's classically
perfect lattice fermion actions. When chiral symmetry is nonlinearly realized
in effective field theories on the lattice, the doubling problem again does not
arise. This review provides an introduction to chiral symmetry on the lattice
with an emphasis on the basic theoretical framework.Comment: (41 pages, to be published in Prog. Part. Nucl. Phys. Vol. 53, issue
1 (2004)
Modeling pion physics in the -regime of two-flavor QCD using strong coupling lattice QED
In order to model pions of two-flavor QCD we consider a lattice field theory
involving two flavors of staggered quarks interacting strongly with U(1) gauge
fields. For massless quarks, this theory has an symmetry. By adding a four-fermion term we can break the U_A(1)
symmetry and thus incorporate the physics of the QCD anomaly. We can also tune
the pion decay constant F, to be small compared to the lattice cutoff by
starting with an extra fictitious dimension, thus allowing us to model low
energy pion physics in a setting similar to lattice QCD from first principles.
However, unlike lattice QCD, a major advantage of our model is that we can
easily design efficient algorithms to compute a variety of quantities in the
chiral limit. Here we show that the model reproduces the predictions of chiral
perturbation theory in the -regime.Comment: 24 pages, 7 figure
Phase-diagram of two-color lattice QCD in the chiral limit
We study thermodynamics of strongly coupled lattice QCD with two colors of
massless staggered fermions as a function of the baryon chemical potential
in 3+1 dimensions using a new cluster algorithm. We find evidence that
the model undergoes a weak first order phase transition at which
becomes second order at a finite . Symmetry considerations suggest that
the universality class of these phase transitions should be governed by an
field theory with collinear order, with N=3 at and
N=2 at . The universality class of the second order phase
transition at appears to be governed by the decoupled XY fixed
point present in the field theory. Finally we show that the
quantum (T=0) phase transition as a function of is a second order mean
field transition.Comment: 31 pages, 12 figure
Quantum Spin Formulation of the Principal Chiral Model
We formulate the two-dimensional principal chiral model as a quantum spin
model, replacing the classical fields by quantum operators acting in a Hilbert
space, and introducing an additional, Euclidean time dimension. Using coherent
state path integral techniques, we show that in the limit in which a large
representation is chosen for the operators, the low energy excitations of the
model describe a principal chiral model in three dimensions. By dimensional
reduction, the two-dimensional principal chiral model of classical fields is
recovered.Comment: 3pages, LATTICE9
- …