arXiv subjects

David Pesznyak

Publications and source records attributed to David Pesznyak.

4 recordsLinked to original sources

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↗

arXiv2026

Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models

We perform a detailed analysis of the fermionic sign problem in a series of one dimensional integrals, that are achieved as extreme (one-site) limits of genuine physics models. Altogether we studied a Hubbard-like, a Gross-Neveu-like, a Thirring-like and a Chern-Simons-like integral. We compare the Lefschetz-thimble structure for these integrals with contours obtained with the holomorphic flow equations at different flow-times and with numerically optimized continuous integration contours, defined by a maximal value of the expectation values of the phases. With the holomorphic flow equation, we perform the large flow-time limit, so that the average phase corresponds to its value on the thimbles. In some of these integrals (the Hubbard-, Gross-Neveu-, and Chern-Simons-like integrals), we observe that the convergence to this value is not monotonic, meaning that there is an optimal flow-time where the sign problem is weaker than it is on the thimbles. Furthermore, we find that for all of these toy models, numerical optimization can find continuous contours on which the sign problem is considerably weaker than it is both on the thimbles and at flowed integration contours at the optimal flow-time.

hep-lat↗

arXiv2023

Fighting the sign problem in a chiral random matrix model with contour deformations

We studied integration contour deformations in the chiral random matrix theory of Stephanov with the goal of alleviating the finite-density sign problem. We considered simple ansätze for the deformed integration contours, and optimized their parameters. We find that optimization of a single parameter manages to considerably improve on the severity of the sign problem. We show numerical evidence that the improvement achieved is exponential in the degrees of freedom of the system, i.e., the size of the random matrix. We also compare the optimization method with contour deformations coming from the holomorphic flow equations.

hep-lat↗

arXiv2021

Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density

The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first-principle lattice simulations to calculate corrections to the ideal HRG. Namely, we determine the sub-leading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential ($μ_B$) - strangeness chemical potential ($μ_S$) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of $N_τ=8,10,12$ using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.

hep-lat↗