Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/9607042

Universal correlations in spectra of the lattice QCD Dirac operator

M. A. Halasz·T. Kalkreuter·J. J. M. Verbaarschot
View original source ↗Read source document ↗Export metadata ↓

Abstract

Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as $12^4$. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal Ensemble for Wilson fermions. In both cases long range spectral fluctuations are strongly suppressed: the variance of a sequence of levels containing $n$ eigenvalues on average is given by $Σ_2(n) \sim 2 (\log n)/βπ^2 $ ($β$ is equal to 4 and 1, respectively) instead of $Σ_2(n) = n$ for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions which differs from Wilson fermions (with the continuum anti-unitary symmetry). For $N_c = 3$, we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. A. Halasz, T. Kalkreuter, J. J. M. Verbaarschot. 1996-07-19. Universal correlations in spectra of the lattice QCD Dirac operator. https://doi.org/10.1016/s0920-5632(96)00632-9

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Properties of the positive and negative parity charm-strange and bottom-strange mesons $D_s$, $D_s^*$, $D_{s0}^*$, $D_{s1}$, $B_s$, $B_s^*$, $B_{s0}^*$, $B_{s1}$ from lattice QCD: masses, decay constants, and compositeness

We present a lattice-QCD determination of properties of the lightest scalar, pseudoscalar, vector, and axial-vector heavy-strange mesons. This includes the decay constants of all mesons, and the binding energies and Weinberg compositeness parameters of the positive-parity states. The calculations are performed with domain-wall fermions for the light and strange quarks and anisotropic clover actions for the charm and bottom quarks. We use seven ensembles generated by RBC/UKQCD with pion masses ranging from 431 MeV to 139 MeV and lattice spacings ranging from 0.114 fm to 0.073 fm, which allows us to perform combined chiral and continuum extrapolations. For the negative-parity mesons, we obtain $f_{D_s}=251.4(2.1)(0.4)(2.5)\:{\rm MeV}$, $f_{D_s^*}=272.5(4.3)(1.0)(2.7)\:{\rm MeV}$, $f_{B_s}=228.4(5.8)(0.5)(2.3)\:{\rm MeV}$, $f_{B_s^*}=229.2(4.4)(0.8)(2.3)\:{\rm MeV}$, $f_{D_s^*}/f_{D_s}=1.086(14)(11)$, and $f_{B_s^*}/f_{B_s}=1.003(22)(10)$. In the positive-parity sector, the finite-volume energies and decay constants are extracted using the GEVP from correlation matrices with three different types of hadron interpolating operators, including operators with covariant derivatives and meson-meson-scattering operators at both source and sink. After extrapolation to the physical point, we obtain $f_{D^*_{s0}}=136.6 (8.0)(4.0)(1.4)$ MeV, $f_{D_{s1}}=200 (33)(24)(2)$ MeV, $f_{B^*_{s0}}=207 (12)(8)(2)$ MeV, and $f_{B_{s1}}= 196 (16)(11)(2)$ MeV. Our results for $f_{B^*_{s0}}$ and $f_{B_{s1}}$ are the first from lattice QCD. L\"uscher's method is used to find the infinite-volume bound-state masses. At the physical point, we obtain $m_{D^*_{s0}}-m_D-m_K=-48 (14)(4)$ MeV, $m_{D_{s1}}-m_{D^*}-m_K=-61 (15)(2)$ MeV, $m_{B^*_{s0}}-m_B-m_K= -69 (13)(4)$ MeV, and $m_{B_{s1}}-m_{B^*}-m_K=-77 (10)(5)$ MeV. Our analysis shows consistency with the positive-parity states being predominantly molecular.

hep-lat↗
arXiv2026

Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories

Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.

hep-lat↗
arXiv2026

Gauge field digitization in the Hamiltonian limit

Quantum computers can circumvent the numerical sign problem in gauge theories at finite density or in real time. Quantum simulations of gauge theories require a finite-dimensional representation of continuous gauge fields. Replacing a continuous gauge group by a finite subgroup can substantially reduce the required quantum resources, but introduces digitization errors that must be controlled in the Hamiltonian, or continuous-time, limit. Previous studies, using the isotropic Euclidean lattices showed that the freezing transition of the discrete subgroup can make it a bad approximation for the continuous group at large Euclidean couplings. Here, we study the digitization of U(1) by its Z($N$) subgroups in 2+1 dimensions using anisotropic Euclidean lattices. We derive the trajectories of the spatial and temporal gauge couplings along which the Hamiltonian limit is approached at fixed Hamiltonian coupling. While the temporal coupling exhibits power-law scaling in the continuous U(1) theory, it grows only logarithmically for finite Z($N$). Using classical lattice simulations and exact diagonalization, we verify that these trajectories reproduce the corresponding Hamiltonian theories. We find that the freezing transition persists in the Hamiltonian limit of discrete gauge groups and that finite-$N$ theories can differ substantially from U(1) even outside the frozen regime, in contrast to the behavior on isotropic Euclidean lattices, where for small couplings, the discrete group provides a very accurate approximation of the continuous group. Our results provide a classical benchmark for quantifying the systematic errors due to gauge-field digitization in quantum simulations.

hep-lat↗