8 research outputs found
Random matrix model of QCD at finite density and the nature of the quenched limit
We use a random matrix model to study chiral symmetry breaking in QCD at
finite chemical potential . We solve the model and compute the eigenvalue
density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails
for : we find that quenched QCD is not a simple limit of QCD
with quarks. It is the limit of a theory with quarks: quarks with
original action and quarks with conjugate action. The results agree with
earlier studies of lattice QCD at and provide a simple analytical
explanation of a long-standing puzzle.Comment: 9 pages, revtex3.0, 4 epsf figures. Packed by "uufiles" script.
Revised version (PRL): minor change
Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
We apply the Glasgow method for lattice QCD at finite chemical potential to a
schematic random matrix model (RMM). In this method the zeros of the partition
function are obtained by averaging the coefficients of its expansion in powers
of the chemical potential. In this paper we investigate the phase structure by
means of Glasgow averaging and demonstrate that the method converges to the
correct analytically known result. We conclude that the statistics needed for
complete convergence grows exponentially with the size of the system, in our
case, the dimension of the Dirac matrix. The use of an unquenched ensemble at
does not give an improvement over a quenched ensemble.
We elucidate the phenomenon of a faster convergence of certain zeros of the
partition function. The imprecision affecting the coefficients of the
polynomial in the chemical potential can be interpeted as the appearance of a
spurious phase. This phase dominates in the regions where the exact partition
function is exponentially small, introducing additional phase boundaries, and
hiding part of the true ones. The zeros along the surviving parts of the true
boundaries remain unaffected.Comment: 17 pages, 14 figures, typos correcte
Fermion determinants in matrix models of QCD at nonzero chemical potential
The presence of a chemical potential completely changes the analytical
structure of the QCD partition function. In particular, the eigenvalues of the
Dirac operator are distributed over a finite area in the complex plane, whereas
the zeros of the partition function in the complex mass plane remain on a
curve. In this paper we study the effects of the fermion determinant at nonzero
chemical potential on the Dirac spectrum by means of the resolvent, G(z), of
the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1)
model (Gibbs model) and in a random matrix model with the global symmetries of
the QCD partition function. In both cases we find that, if the argument z of
the resolvent is not equal to the mass m in the fermion determinant, the
resolvent diverges in the thermodynamic limit. However, for z =m the resolvent
in both models is well defined. In particular, the nature of the limit is illuminated in the Gibbs model. The phase structure of the
random matrix model in the complex m and \mu-planes is investigated both by a
saddle point approximation and via the distribution of Yang-Lee zeros. Both
methods are in complete agreement and lead to a well-defined chiral condensate
and quark number density.Comment: 27 pages, 6 figures, Late
Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
In quantum chromodynamics (QCD) at nonzero chemical potential, the
eigenvalues of the Dirac operator are scattered in the complex plane. Can the
fluctuation properties of the Dirac spectrum be described by universal
predictions of non-Hermitian random matrix theory? We introduce an unfolding
procedure for complex eigenvalues and apply it to data from lattice QCD at
finite chemical potential to construct the nearest-neighbor spacing
distribution of adjacent eigenvalues in the complex plane. For intermediate
values of , we find agreement with predictions of the Ginibre ensemble of
random matrix theory, both in the confinement and in the deconfinement phase.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
Instantons and the Chiral Phase Transition at non-zero Baryon Density
We study an interacting ensemble of instantons at finite baryon chemical
potential. We emphasize the importance of fermionic zero modes and calculate
the fermion induced interaction between instantons at non-zero chemical
potential. We show that unquenched simulations of the instanton ensemble are
feasible in two regimes, for sufficiently small and for very large chemical
potential. At very large chemical potential chiral symmetry is restored and the
instanton ensemble is dominated by strongly correlated chain-like
configurations.Comment: 37 pages, 10 figures, uses revtex, revised version (minor corrections
and expanded dicussion