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Shailesh Chandrasekharan

Publications and source records attributed to Shailesh Chandrasekharan.

103 records · Page 6Linked to original sources
arXiv2000

A Chiral Phase Transition using a Fermion Cluster Algorithm

The recent solution to the fermion sign problem allows, for the first time, the use of cluster algorithm techniques to compute certain fermionic path integrals. To illustrate the underlying ideas behind the progress, a cluster algorithm is constructed to study the chiral phase transition in a strongly interacting staggered fermion model with an arbitrary mass term in 3+1 dimensions. Unlike conventional methods there is no difficulty in the cluster method to approach the chiral (massless) limit. Results using the new algorithm confirm that the chiral transition falls under the expected universality class.

hep-lat↗
arXiv1999

Meron-Cluster Solution of Fermion Sign Problems

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

cond-mat.stat-mech↗
arXiv1999

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.

hep-lat↗
arXiv1999

Lattice QCD with Ginsparg-Wilson fermions

Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson relation, is perhaps the best known formulation of QCD with a finite cutoff. It reproduces all the low energy QCD phenomenology associated with chiral symmetry at finite lattice spacings. In particular it explains the origin of massless pions due to spontaneous chiral symmetry breaking and leads to new ways to approach the U(1) problem on the lattice. Here we show these results in the path integral formulation and derive for the first time in lattice QCD a known formal continuum relation between the chiral condensate and the topological susceptibility. This relation leads to predictions for the critical behavior of the topological susceptibility near the phase transition and can now be checked in Monte-Carlo simulations even at finite lattice spacings.

hep-lat↗
arXiv1999

Non-perturbative Renormalization Constants using Ward Identities

We extend the application of axial Ward identities to calculate $b_A, b_P$ and $b_T$, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the O(a) improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are undetermined. We present results of a pilot numerical study using hadronic correlators.

hep-lat↗
arXiv1998

Ginsparg-Wilson Fermions: A study in the Schwinger Model

Qualitative features of Ginsparg-Wilson fermions, as formulated by Neuberger, coupled to two dimensional U(1) gauge theory are studied. The role of the Wilson mass parameter in changing the number of massless flavors in the theory and its connection with the index of the Dirac operator is studied. Although the index of the Dirac operator is not related to the geometric definition of the topological charge for strong couplings, the two start to agree as soon as one goes to moderately weak couplings. This produces the desired singularity in the quenched chiral condensate which appears to be very difficult to reproduce with staggered fermions. The fermion determinant removes the singularity and reproduces the known chiral condensate and the meson mass within understandable errors.

hep-lat↗
arXiv1998

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.

hep-lat↗
arXiv1998

Anomalous Chiral Symmetry Breaking above the QCD Phase Transition

We study the anomalous breaking of U_A(1) symmetry just above the QCD phase transition for zero and two flavors of quarks, using a staggered fermion, lattice discretization. The properties of the QCD phase transition are expected to depend on the degree of U_A(1) symmetry breaking in the transition region. For the physical case of two flavors, we carry out extensive simulations on a 16^3 x 4 lattice, measuring a difference in susceptibilities which is sensitive to U_A(1) symmetry and which avoids many of the staggered fermion discretization difficulties. The results suggest that anomalous effects are at or below the 15% level.

hep-lat↗
arXiv1996

A Large N Chiral Transition on a Plaquette

We construct a model of a chiral transition using the well known large N transition in two dimensional U(N) lattice gauge theory. Restricting the model to a single plaquette, we introduce Grassmann variables on the corners of the plaquette with the natural phase factors of staggered fermions and couple them to the U(N) link variables. The classical theory has a continuous chiral symmetry which is broken at strong couplings, but is restored for weak couplings in the $N \to \infty$ limit.

hep-th↗
arXiv1995

$Z_3$ Twisted Chiral Condensates in QCD at Finite Temperatures

It was recently observed in a lattice QCD measurement that the chiral condensate in the quenched approximation shows dramatically different behavior in the three $Z_3$-equivalent de-confined phases. We argue that this phenomenon can be understood qualitatively as an effect of $Z_3$ twists on fermionic fields. Quarks under these $Z_3$-twists become global anyons and hence display different thermodynamic properties. We further show that the lattice data can be roughly modeled by a Nambu-Jona-Lasinio type Lagrangian with a minimal coupling to a constant gauge field $A_0=2πnT/3$ (with $n=0$, $\pm1$), which arises naturally from the non-trivial phase of the Polyakov line.

hep-ph↗
arXiv1995

Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

The QCD phase transition is studied on $16^3$ and $32^3 \times 4$ lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark $ζ$ and study the resulting chiral condensate, $\azbz$ as a function of the $ζ$ mass, $m_ζ$. By examining $\azbz$ for $10^{-10} \le m_ζ\le 10$ we gain considerable information about the spectrum of Dirac eigenvalues. A comparison of $ma=0.01$ and 0.025 shows little dependence of the Dirac spectrum on such a light, dynamical quark mass, after an overall shift in $β$ is removed. The presence of sufficient small eigenvalues to support anomalous chiral symmetry breaking in the high temperature phase is examined quantitatively. In an effort to enhance these small eigenvalues, $\azbz$ is also examined in the pure gauge theory in the region of the deconfinement transition with unexpected results. Above the critical temperature, the three $Z_3$ phases show dramatically different chiral behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a system with one flavor of staggered fermion at $N_t=4$ will possess a chiral a phase transition---behavior not expected in the continuum limit.

hep-lat↗
arXiv1993

Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass

A Fermion in 2+1 dimensions, with a mass function which depends on one spatial coordinate and passes through a zero ( a domain wall mass), is considered. In this model, originally proposed by Callan and Harvey, the gauge variation of the effective gauge action mainly consists of two terms. One comes from the induced Chern-Simons term and the other from the chiral fermions, bound to the 1+1 dimensional wall, and they are expected to cancel each other. Though there exist arguments in favour of this, based on the possible forms of the effective action valid far from the wall and some facts about theories of chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this paper we present an explicit calculation of this cancellation at one loop valid even close to the wall. We show that, integrating out the ``massive'' modes of the theory does produce the Chern-Simons term, as appreciated previously. In addition we show that it generates a term that softens the high energy behaviour of the 1+1 dimensional effective chiral theory thereby resolving an ambiguity present in a general 1+1 dimensional theory.

hep-th↗