Tue·Nov 8, 2022Tuesday·November 8, 2022

1. 01*

   Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation

   Di Luo🇺🇸 · Shunyue Yuan🇺🇸 · James Stokes🇺🇸 · Bryan K. Clark🇺🇸

   Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.

   hep-latcond-mat.dis-nncond-mat.str-elcs.LG+122 citations
2. 02*

   Fourier-Flow model generating Feynman paths

   Shile Chen🇨🇳 · Oleh Savchuk🇺🇦 · Shiqi Zheng🇨🇳 · Baoyi Chen🇨🇳 · Horst Stoecker🇩🇪 · Lingxiao Wang🇩🇪 · Kai Zhou🇩🇪

   As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates into a weighted sum over all possible paths. The underlying difficulty is to tackle the whole path manifold from finite samples that can effectively represent the Feynman propagator dictated probability distribution. Modern generative models in machine learning can handle learning and representing probability distribution with high computational efficiency. In this study, we propose a Fourier-flow generative model to simulate the Feynman propagator and generate paths for quantum systems. As demonstration, we validate the path generator on the harmonic and anharmonic oscillators. The latter is a double-well system without analytic solutions. To preserve the periodic condition for the system, the Fourier transformation is introduced into the flow model to approach a Matsubara representation. With this novel development, the ground-state wave function and low-lying energy levels are estimated accurately. Our method offers a new avenue to investigate quantum systems with machine learning assisted Feynman Path integral solving.

   hep-lathep-thquant-phPRD(2023)·27 citations
3. 03*

   Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement

   Claudio Bonati🇮🇹 · Niccolò Francini🇮🇹

   We study the phase diagram and phase transitions of the three dimensional multicomponent lattice Higgs model with non-compact Abelian discrete groups. The model with non-compact U(1) gauge group is known to undergo, for a sufficiently large number of scalar fields $N$, a continuous transition associated to the charged fixed point of the continuous Abelian Higgs field theory. We show that in the model with gauge group ${\mathbb{Z}}_q^{(nc)}\equiv 2\pi \mathbb{Z}/q$ only critical transitions in the orthogonal universality classes are present for small values of $N$, while a symmetry enlargement to the continuous Abelian Higgs universality class happens when $q\ge 5$ and $N$ is large enough.

   hep-latcond-mat.stat-mechPRB(2023)·6 citations
4. 04*

   Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions

   Gunnar S. Bali🇩🇪 · Sara Collins🇩🇪 · Peter Georg🇩🇪 · Daniel Jenkins🇩🇪 · Piotr Korcyl🇵🇱 · Andreas Schäfer🇩🇪 · Enno E. Scholz🇩🇪 · Jakob Simeth🇩🇪 · Wolfgang Söldner🇩🇪 · Simon Weishäupl🇩🇪

   We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing $N_f=2+1$ flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from $a\approx 0.10$fm down to below $0.04$fm. The light pion mass varies from $M_{\pi }\approx 429$MeV down to $127$MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than $2.3$fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales $\sqrt{t_{0,\mathrm{ph}}}=0.1449_{(9)}^{(7)}$fm and $t_0^{\ast }\approx t_{0,\mathrm{ph}}$ from the octet cascade ($\Xi$ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass $m_N=941.7_{(7.6)}^{(6.5)}$MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the $\Omega$ baryon sigma~terms ${\sigma }_{\pi N}=43.9(4.7)$MeV, ${\sigma }_{\pi \Lambda }=28.2_{(5.4)}^{(4.3)}$MeV, ${\sigma }_{\pi \Sigma }=25.9_{(6.1)}^{(3.8)}$MeV, ${\sigma }_{\pi \Xi }=11.2_{(6.4)}^{(4.5)}$MeV and ${\sigma }_{\pi \Omega }=6.9_{(4.3)}^{(5.3)}$MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.

   hep-lathep-phJHEP(2023)·90 citations
5. 05*

   Optimised Trotter Decompositions for Classical and Quantum Computing

   Johann Ostmeyer🇬🇧

   Suzuki-Trotter decompositions of exponential operators like $\exp (Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H={\sum }_k{A}_k$, for instance as local gates on quantum computers. We demonstrate how highly optimised schemes originally derived for exactly two operators $A_{1,2}$ can be applied to such generic Suzuki-Trotter decompositions, providing a formal proof of correctness as well as numerical evidence of efficiency. A comprehensive review of existing symmetric decomposition schemes up to order $n\le 4$ is presented and complemented by a number of novel schemes, including both real and complex coefficients. We derive the theoretically most efficient unitary and non-unitary 4th order decompositions. The list is augmented by several exceptionally efficient schemes of higher order $n\le 8$. Furthermore we show how Taylor expansions can be used on classical devices to reach machine precision at a computational effort at which state of the art Trotterization schemes do not surpass a relative precision of $10^{-4}$. Finally, a short and easily understandable summary explains how to choose the optimal decomposition in any given scenario.

   ↳ quant-phcond-mat.stat-mechcond-mat.str-elhep-lat+1J.Phys.A(2023)·64 citations
6. 06*

   Geometric confinement in gauge theories

   Alexander D. Popov🇩🇪

   In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field $\rho$ which tends to zero outside some compact region $S\subset {\mathbb{R}}^3$ determined dynamically from the equations of motion. The gauge coupling in the soliton bag model is running as the inverse power of $\rho$ already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric $\mathrm{d}{s}_M^2+{\rho }^2\mathrm{d}{s}_G^2$ on the principal $G$-bundle $P(M,G)\cong M\times G$ with a non-Abelian group $G$ over Minkowski space $M={\mathbb{R}}^{3,1}$. Confinement of quarks and gluons in a compact domain $S\subset {\mathbb{R}}^3$ is a consequence of the collapse of the bundle manifold $M\times G$ to $M$ outside $S$ due to shrinking of the group manifold $G$ to a point. We describe the formation of such regions $S$ as a dynamical process controlled by the order parameter field $\rho$.

   ↳ hep-thhep-lathep-phnucl-thSymmetry(2023)·1 citation
7. 07*

   A coupled-channel system with anomalous thresholds and unitarity

   Csaba L. Korpa🇭🇺 · Matthias F.M. Lutz🇩🇪 · Xiao-Yu Guo🇨🇳 · Yonggoo Heo🇩🇪

   We consider the isospin one-half example system, with $D\pi ,D\eta ,D_s\bar{K},D^{\ast }\pi ,D^{\ast }\eta ,D^{\ast }\bar{K}$ coupled channels in the $J^P=1^{-}$ partial wave, chosen such that various phenomena that come with the opening of an anomalous threshold can be illustrated in a step-wise procedure by a suitable variation of up, down and strange quark masses. We use a set of LEC in the chiral Lagrangian that were adjusted to a large set of Lattice QCD results. The six phase shifts and inelasticity parameters are presented for various choices of the pion mass. For a pion mass of 150 MeV there are no anomalous thresholds encountered. The small change from 150 MeV to 145 MeV pion mass causes a dramatic impact of the anomalous threshold on the phase shifts.

   ↳ hep-phhep-latnucl-thPRD(2023)·10 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.