672 research outputs found
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
Finding the Pion in the Chiral Random Matrix Vacuum
The existence of a Goldstone boson is demonstrated in chiral random matrix
theory. After determining the effective coupling and calculating the scalar and
pseudoscalar propagators, a random phase approximation summation reveals the
massless pion and massive sigma modes expected whenever chiral symmetry is
spontaneously broken.Comment: 3 pages, 1 figure, revte
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
Three-dimensional QCD in the adjoint representation and random matrix theory
In this paper we complete the derivations of finite volume partition
functions for QCD using random matrix theories by calculating the effective
low-energy partition function for three-dimensional QCD in the adjoint
representation from a random matrix theory with the same global symmetries. As
expected, this case corresponds to Dyson index , that is, the Dirac
operator can be written in terms of real quaternions. After discussing the
issue of defining Majorana fermions in Euclidean space, the actual matrix model
calculation turns out to be simple. We find that the symmetry breaking pattern
is , as expected from the correspondence
between symmetric (super)spaces and random matrix universality classes found by
Zirnbauer. We also derive the first Leutwyler--Smilga sum rule.Comment: LaTeX, 19 pages. Minor corrections, added comments, to appear on
Phys. Rev.
Universal Massive Spectral Correlators and QCD_3
Based on random matrix theory in the unitary ensemble, we derive the
double-microscopic massive spectral correlators corresponding to the Dirac
operator of QCD_3 with an even number of fermions N_f. We prove that these
spectral correlators are universal, and demonstrate that they satisfy exact
massive spectral sum rules of QCD_3 in a phase where flavor symmetries are
spontaneously broken according to U(N_f) -> U(N_f/2) x U(N_f/2).Comment: 5 pages, REVTeX. Misprint correcte
Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory
The low-lying spectrum of the Dirac operator is predicted to be universal,
within three classes, depending on symmetry properties specified according to
random matrix theory. The three universal classes are the orthogonal, unitary
and symplectic ensemble. Lattice gauge theory with staggered fermions has
verified two of the cases so far, unitary and symplectic, with staggered
fermions in the fundamental representation of SU(3) and SU(2). We verify the
missing case here, namely orthogonal, with staggered fermions in the adjoint
representation of SU(N_c), N_c=2, 3.Comment: 3 pages, revtex, 2 postscript figure
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
- …