213 research outputs found
Matrix model correlation functions and lattice data for the QCD Dirac operator with chemical potential
We apply a complex chiral random matrix model as an effective model to QCD
with a small chemical potential at zero temperature. In our model the correlation
functions of complex eigenvalues can be determined analytically in two different
limits, at weak and strong non-Hermiticity. We compare them to the distribution
of the smallest Dirac operator eigenvalues from quenched QCD lattice data for
small values of the chemical potential, appropriately rescaled with the volume.
This confirms the existence of two different scaling regimes from lattice data
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
We solve a random two-matrix model with two real asymmetric matrices whose
primary purpose is to describe certain aspects of quantum chromodynamics with
two colours and dynamical fermions at nonzero quark chemical potential mu. In
this symmetry class the determinant of the Dirac operator is real but not
necessarily positive. Despite this sign problem the unquenched matrix model
remains completely solvable and provides detailed predictions for the Dirac
operator spectrum in two different physical scenarios/limits: (i) the
epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied
by the volume remains fixed in the infinite-volume limit and (ii) the
high-density regime where a BCS gap is formed and mu is unscaled. We give
explicit examples for the complex, real, and imaginary eigenvalue densities
including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate
masses has no sign problem and can be tested with standard lattice techniques,
we analyse the severity of the sign problem for non-degenerate masses as a
function of the mass split and of mu.
On the mathematical side our new results include an analytical formula for
the spectral density of real Wishart eigenvalues in the limit (i) of weak
non-Hermiticity, thus completing the previous solution of the corresponding
quenched model of two real asymmetric Wishart matrices.Comment: 45 pages, 31 figures; references added, as published in JHE
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Individual complex Dirac eigenvalue distributions from random matrix theory and lattice QCD at nonzero chemical potential
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero chemical potential are distributed in the complex plane. Exact and approximate analytical results for such distributions are derived from non-Hermitian random matrix theory. When comparing these to lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class
Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results
For QCD at non-zero chemical potential , the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from random matrix theory (RMT). We distinguish two cases depending on the parameter , where is the volume and is the familiar low-energy constant of chiral perturbation theory. For small , we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large , all spectral correlations are rotationally invariant, and exact results can be derived. We compare the RMT predictions to lattice data and in both cases find excellent agreement in the topological sectors
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