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

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

Chiral and Critical Behavior in Strong Coupling QCD

We use a cluster algorithm to study the critical behavior of strongly coupled lattice QCD in the chiral limit. We show that the finite temperature chiral phase transition belongs to the O(2) universality class as expected. When we compute the finite size effects of the chiral susceptibility in the low temperature phase close to the transition, we find clear evidence for chiral singularities predicted by chiral perturbation theory (ChPT). On the other hand it is difficult to reconcile the quark mass dependence of various quantities near the chiral limit with ChPT.Comment: 3 Pages, 3 figures, Lattice2003(nonzero

Confinement, Chiral Symmetry Breaking and Continuum Limits in Quantum Link Models

Using the example of compact U(1) lattice gauge theory we argue that quantum link models can be used to reproduce the physics of conventional Hamiltonian lattice gauge theories. In addition to the usual gauge coupling $g$, these models have a new parameter $j$ which naturally cuts-off large electric flux quanta on each link while preserving exact U(1) gauge invariance. The $j\to\infty$ limit recovers the conventional Hamiltonian. At strong couplings, the theory shows confinement and chiral symmetry breaking for all non-trivial values of $j$. The phase diagram of the 3+1 dimensional theory suggests that a coulomb phase is present at large but finite $j$. Setting $g=0$, a new approach to the physics of compact U(1) gauge theory on the lattice emerges. In this case the parameter $j$ takes over the role of the gauge coupling, and $j\to \infty$ describes free photons.Comment: LATTICE98(spin

Fermion Cluster Algorithms

Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion world lines. This solution leads to the possibility of designing fermion cluster algorithms in certain cases. Using the example of free non-relativistic fermions we discuss the ideas underlying the algorithm.Comment: LATTICE99 (algorithms & Machines), 3 pages, 4 eps figures, espcrc2.st