1,098 research outputs found

### Anomalous superfluidity in 2+1 dimensional two-color lattice QCD

We study thermodynamics of strongly coupled lattice QCD with $two$ colors of
staggered fermions in $(2+1)$ dimensions. The partition function of this model
can be written elegantly as a statistical mechanics of dimers and baryonloops.
The model is invariant under an $SO(3)\times U(1)$ symmetry. At low
temperatures we find evidence for superfluidity in the U(1) symmetry sector
while the SO(3) symmetry remains unbroken. The finite temperature phase
transition appears to belong to the Kosterlitz-Thouless universality class, but
the superfluid density jump $\rho_s(T_c)$ at the critical temperature $T_c$ is
anomalously higher than the normal value of $2 T_c/\pi$. We show that by adding
a small SO(3) symmetry breaking term to the model, the superfluid density jump
returns to its normal value implying that the extra symmetry causes anomalous
superfluid behavior. Our results may be of interest to researchers studying
superfluidity in spin-1 systems.Comment: Minor revisions. Added a paragraph. to be published in PR

### Fermion bag solutions to some sign problems in four-fermion field theories

Lattice four-fermion models containing $N$ flavors of staggered fermions,
that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer
from sign problems when formulated using the auxiliary field approach. Although
these problems have been ignored in previous studies, they can be severe. Here
we show that the sign problems disappear when the models are formulated in the
fermion bag approach, allowing us to solve them rigorously for the first time.Comment: references adde

### 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 $U$ 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 $U$ 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 $\nu=0.87(2)$ and $\eta=0.62(2)$.Comment: 31 pages, 9 figures, 5 table

### 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

### 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
$\mu$ 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 $\mu$-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

### 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
$\mu$ in 3+1 dimensions using a new cluster algorithm. We find evidence that
the model undergoes a weak first order phase transition at $\mu=0$ which
becomes second order at a finite $\mu$. Symmetry considerations suggest that
the universality class of these phase transitions should be governed by an
$O(N)\times O(2)$ field theory with collinear order, with N=3 at $\mu=0$ and
N=2 at $\mu \neq 0$. The universality class of the second order phase
transition at $\mu\neq 0$ appears to be governed by the decoupled XY fixed
point present in the $O(2)\times O(2)$ field theory. Finally we show that the
quantum (T=0) phase transition as a function of $\mu$ is a second order mean
field transition.Comment: 31 pages, 12 figure

### An Introduction to Chiral Symmetry on the Lattice

The $SU(N_f)_L \otimes SU(N_f)_R$ 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)

### 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

### Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at
finite density in terms of dual variables, i.e., loops of flux and surfaces. In
the dual representation the complex action problem of the conventional
formulation is resolved and Monte Carlo simulations at arbitrary chemical
potential become possible. A suitable algorithm based on plaquette occupation
numbers and link-fluxes is introduced and we analyze the model at zero
temperature and finite density both in the weak and strong coupling phases. We
show that at zero temperature the model has different first order phase
transitions as a function of the chemical potential both for the weak and
strong coupling phases. The exploratory study demonstrates that alternative
degrees of freedom may successfully be used for Monte Carlo simulations in
several systems with gauge and matter fields.Comment: Typos corrected and some statements refined. Final version to appear
in Phys. Rev.

### Solutions to sign problems in lattice Yukawa models

We prove that sign problems in the traditional approach to some lattice
Yukawa models can be completely solved when the fermions are formulated using
fermion bags and the bosons are formulated in the worldline representation. We
prove this within the context of two examples of three dimensional models,
symmetric under $U_L(1) \times U_R(1) \times Z_2 ({Parity})$ transformations,
one involving staggered fermions and the other involving Wilson fermions. We
argue that these models have interesting quantum phase transitions that can now
be studied using Monte Carlo methods.Comment: 5 pages, 1 figure (Fixed minor typographical errors, expanded the
discussion to include solution to the sign problem with the conventional
bosonic action and added a reference.

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