807 research outputs found
Quantum chaos in QCD at finite temperature
We study complete eigenvalue spectra of the staggered Dirac matrix in
quenched QCD on a lattice. In particular, we investigate the
nearest-neighbor spacing distribution for various values of both
in the confinement and deconfinement phase. In both phases except far into the
deconfinement region, the data agree with the Wigner surmise of random matrix
theory which is indicative of quantum chaos. No signs of a transition to
Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at
"Lattice 97", to appear in the proceeding
Quantum chaos and QCD at finite chemical potential
We investigate the distribution of the spacings of adjacent eigenvalues of
the lattice Dirac operator. At zero chemical potential , the
nearest-neighbor spacing distribution follows the Wigner surmise of
random matrix theory both in the confinement and in the deconfinement phase.
This is indicative of quantum chaos. At nonzero chemical potential, the
eigenvalues of the Dirac operator become complex. We discuss how can be
defined in the complex plane. Numerical results from an SU(3) simulation with
staggered fermions are compared with predictions from non-hermitian random
matrix theory, and agreement with the Ginibre ensemble is found for .Comment: LATTICE98(hightemp), 3 pages, 10 figure
Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid
The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H3LiIr2O6 has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H3LiIr2O6
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
Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state
Lack of Lorentz invariance of QCD at finite quark chemical potential in
general implies the need of Lorentz non-invariant condensates for the
self-consistent description of the color-superconducting ground state.
Moreover, the spontaneous breakdown of color SU(3) in this state naturally
leads to the existence of SU(3) non-invariant non-superconducting expectation
values. We illustrate these observations by analyzing the properties of an
effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the
possibility of color-superconducting states with effectively gapless fermionic
excitations. It turns out that the effect of condensates so far neglected can
yield new interesting phenomena.Comment: 16 pages, 3 figure
Imaginary chemical potential and finite fermion density on the lattice
Standard lattice fermion algorithms run into the well-known sign problem at
real chemical potential. In this paper we investigate the possibility of using
imaginary chemical potential, and argue that it has advantages over other
methods, particularly for probing the physics at finite temperature as well as
density. As a feasibility study, we present numerical results for the partition
function of the two-dimensional Hubbard model with imaginary chemical
potential.
We also note that systems with a net imbalance of isospin may be simulated
using a real chemical potential that couples to I_3 without suffering from the
sign problem.Comment: 9 pages, LaTe
Quantum Chaos in Compact Lattice QED
Complete eigenvalue spectra of the staggered Dirac operator in quenched
compact QED are studied on and lattices. We
investigate the behavior of the nearest-neighbor spacing distribution as
a measure of the fluctuation properties of the eigenvalues in the strong
coupling and the Coulomb phase. In both phases we find agreement with the
Wigner surmise of the unitary ensemble of random-matrix theory indicating
quantum chaos. Combining this with previous results on QCD, we conjecture that
quite generally the non-linear couplings of quantum field theories lead to a
chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure
Impossibility of spontaneously breaking local symmetries and the sign problem
Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.Comment: Latex 6 page
On the Phase Diagram of QCD
We analyze the phase diagram of QCD with two massless quark flavors in the
space of temperature, T, and chemical potential of the baryon charge, mu, using
available experimental knowledge of QCD, insights gained from various models,
as well as general and model independent arguments including continuity,
universality, and thermodynamic relations. A random matrix model is used to
describe the chiral symmetry restoration phase transition at finite T and mu.
In agreement with general arguments, this model predicts a tricritical point in
the T mu plane. Certain critical properties at such a point are universal and
can be relevant to heavy ion collision experiments.Comment: 21 pages, version to appear in Phys. Rev. D (2 references added
Quantum Chaos in the Yang-Mills-Higgs System at Finite Temperature
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is
studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs
is calculated within thermofield dynamics. Level statistics of the spectra is
studied by plotting nearest-level spacing distribution histograms. It is found
that finite temperature effects lead to a strengthening of chaotic effects,
i.e. spectrum which has Poissonian distribution at zero temperature has
Gaussian distribution at finite-temperature.Comment: 6 pages, 5 figures, Revte
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