arXiv subjects

Michael G. Endres

Publications and source records attributed to Michael G. Endres.

At least 19 recordsLinked to original sources

arXiv2018

Scaling properties of multiscale equilibration

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on non-topological long-distance observables in pure SU(3) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

hep-lat↗

arXiv2016

New simulation strategies for lattice gauge theory

Despite the numerous successful applications of lattice QCD in nuclear and particle theory, fundamental algorithmic challenges remain. Among those, relevant for numerical studies of QCD on a space-time torus, is topological freezing--a form of critical slowing down, which becomes particularly acute for lattice spacings less than 0.05 fm. In these proceedings, I highlight several recently proposed simulation strategies for ameliorating the problem of topological freezing, and discuss both their advantages and disadvantages. Then, I turn focus toward potential strategies for addressing critical slowing down in a more general context.

hep-lat↗

arXiv2016

Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors

We demonstrate the applicability of a recently proposed multiscale thermalization algorithm to two-color quantum chromodynamics (QCD) with two mass-degenerate fermion flavors. The algorithm involves refining an ensemble of gauge configurations that had been generated using a renormalization group (RG) matched coarse action, thereby producing a fine ensemble that is close to the thermalized distribution of a target fine action; the refined ensemble is subsequently rethermalized using conventional algorithms. Although the generalization of this algorithm from pure Yang-Mills theory to QCD with dynamical fermions is straightforward, we find that in the latter case, the method is susceptible to numerical instabilities during the initial stages of rethermalization when using the hybrid Monte Carlo algorithm. We find that these instabilities arise from large fermion forces in the evolution, which are attributed to an accumulation of spurious near-zero modes of the Dirac operator. We propose a simple strategy for curing this problem, and demonstrate that rapid thermalization--as probed by a variety of gluonic and fermionic operators--is possible with the use of this solution. In addition, we study the sensitivity of rethermalization rates to the RG matching of the coarse and fine actions, and identify effective matching conditions based on a variety of measured scales.

hep-lat↗

arXiv2016

Massive photons: an infrared regularization scheme for lattice QCD+QED

Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions.

hep-lat↗

arXiv2015

Photon mass term as an IR regularization for QCD+QED on the lattice

Inclusion of QED in lattice QCD calculations can lead to power-law volume artifacts as a consequence of the long-range nature of the interaction. Such artifacts must be removed by extrapolation in order to attain reliable infinite volume estimates of observables and quantities derived from them. As an alternative to this methodology, we consider the use of a photon mass term as an infrared regulator for QCD+QED, and explore the viability of its use in determining hadron mass shifts and splittings.

hep-lat↗

arXiv2015

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.

hep-lat↗

arXiv2014

Signal/noise optimization strategies for stochastically estimated correlation functions

Numerical studies of quantum field theories usually rely upon an accurate determination of stochastically estimated correlation functions in order to extract information about the spectrum of the theory and matrix elements of operators. The reliable determination of such correlators is often hampered by an exponential degradation of signal/noise at late time separations. We demonstrate that it is sometimes possible to achieve significant enhancements of signal/noise by appropriately optimizing correlators with respect to the source and sink interpolating operators, and highlight the large range of possibilities that are available for this task. The ideas are discussed for both a toy model, and single hadron correlators in the context of quantum chromodynamics.

hep-lat↗

arXiv2014

Signal/noise enhancement strategies for stochastically estimated correlation functions

We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic two-state system, and then explore the practical applicability of the method for single hadron correlators in lattice quantum chromodynamics. In the latter case, we determine the ground state energies of the pion, proton, and delta baryon, as well as the ground and first excited state energy of the rho meson using matrices of correlators computed on an exemplary ensemble of anisotropic gauge configurations. In the majority of cases, we find a modest reduction in the statistical uncertainties on extracted energies compared to conventional variational techniques. However, in the case of the delta baryon, we achieve a factor of three reduction in statistical uncertainties. The variety of outcomes achieved for single hadron correlators illustrates an inherent dependence of the method on the properties of the system under consideration and the operator basis from which the correlators are constructed.

hep-lat↗

arXiv2013

SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.

hep-th↗

arXiv2013

Numerical study of unitary fermions in one spatial dimension

I perform lattice Monte Carlo studies of universal four-component fermion systems in one spatial dimension. Continuum few-body observables (i.e., ground-state energies and integrated contact densities) are determined for both unpolarized and polarized systems of up to eight fermions confined to a harmonic trap. Estimates of the continuum energies for four and five trapped fermions show agreement with exact analytic calculations to within approximately one percent statistical uncertainties. Continuum many-body observables are determined for unpolarized systems of up to 88 fermions confined to a finite box, and 56 fermions confined to a harmonic trap. Results are reported for universal quantities such as the Bertsch parameter, defined as the energy of the untrapped many-body system in units of the corresponding free-gas energy, and its subleading correction at large but finite scattering length. Two independent estimates of these quantities are obtained from thermodynamic limit extrapolations of continuum extrapolated observables. A third estimate of the Bertsch parameter is obtained by combining estimates of the untrapped and trapped integrated contact densities with additional theoretical input from a calculation based on Thomas-Fermi theory. All estimates of the Bertsch parameter and its subleading correction are found to be consistent to within approximately one percent statistical uncertainties. Finally, the continuum restoration of virial theorems is verified for both few- and many-body systems confined to a trap.

hep-lat↗

arXiv2013

Lattice Monte Carlo calculations for unitary fermions in a finite box

We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a finite box using a highly improved lattice action for nonrelativistic spin 1/2 fermions. We obtain a value of $0.366^{+0.016}_{-0.011}$ for the Bertsch parameter, defined as the energy of the unitary Fermi gas measured in units of the free gas energy in the thermodynamic limit. In addition, for up to four unitary fermions, we compute the spectrum of the lattice theory by exact diagonalization of the transfer matrix projected onto irreducible representations of the octahedral group for small to moderate size lattices, providing an independent check of our few-body simulation results. We compare our exact numerical and simulation results for the spectrum to benchmark studies of other research groups, as well as perform an extended analysis of our lattice action improvement scheme, including an analysis of the errors associated with higher partial waves and finite temporal discretization.

hep-lat↗

arXiv2012

Transdimensional equivalence of universal constants for Fermi gases at unitarity

I present lattice Monte Carlo calculations for a universal four-component Fermi gas confined to a finite box and to a harmonic trap in one spatial dimension. I obtain the values xi_1d = 0.370(4) and xi_1d = 0.372(1), respectively, for the Bertsch parameter, a nonperturbative universal constant defined as the (square of the) energy of the untrapped (trapped) system measured in units of the free gas energy. The Bertsch parameter for the one-dimensional system is consistent to within ~1% uncertainties with the most recent numerical and experimental estimates of the analogous Bertsch parameter for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests the intriguing possibility that there exists a universality between two conformal theories in different dimensions. To lend support to this study, I also compute continuum extrapolated ground state energies for four and five fermions confined to a harmonic trap and demonstrate the restoration of a Virial theorem in the continuum limit. The continuum few-body energies obtained are consistent with exact analytical calculations to within ~1.0% and ~0.25% statistical uncertainties, respectively.

hep-lat↗

arXiv2012

Unified contraction algorithm for multi-baryon correlators on the lattice

We propose a novel algorithm for calculating multi-baryon correlation functions on the lattice. By considering the permutation of quarks (Wick contractions) and color/spinor contractions simultaneously, we construct a unified index list for the contraction where the redundancies in the original contraction are eliminated. We find that a significant reduction in the computational cost of correlators is achieved, e.g., by a factor of 192 for $^3$H and $^3$He nuclei, and a factor of 20736 for the $^4$He nucleus, without assuming isospin symmetry. A further reduction is possible by exploiting isospin symmetry, and/or interchange symmetries associated with sink baryons, if such symmetries exist. Extensions for systems with hyperons are presented as well.

hep-lat↗

arXiv2012

Lattice theory for nonrelativistic fermions in one spatial dimension

I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign problem" irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength. This property is in sharp contrast with the analogous three-dimensional two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions. The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study. Positivity of the probability measure for the partition function allows for a mean-field treatment of the model; here, I present such an analysis for the interacting Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit, and demonstrate that there exists a phase in which a continuum limit may be defined.

hep-lat↗

arXiv2011

Listening to Noise

We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions and for baryons in QCD.

hep-lat↗

arXiv2011

Extended study for unitary fermions on a lattice using the cumulant expansion technique

A recently developed lattice method for large numbers of strongly interacting nonrelativistic fermions exhibits a heavy tail in the distributions of correlators for large Euclidean time τ and large number of fermions N, which only allows the measurement of ground state energies for a limited number of fermions using standard techniques. In such cases, it is suggested that measuring the log of the correlator is more efficient, and a cumulant expansion of this quantity can be exactly related to the correlation function. The cumulant expansion technique allows us to determine the ground state energies of up to 66 unpolarized unitary fermions on lattices as large as 72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic potential on lattices as large as 72$\times$64^3. We have also improved our lattice action with a Galilean invariant form for the four-fermion interaction, which results in predictive volume scaling of the lowest energy of three fermions in a periodic box and in good agreement of our results for N \leq 6 trapped unitary fermions with those from other benchmark calculations.

hep-lat↗

arXiv2011

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions, and apply it to a dilute gas of unitary fermions confined to a harmonic trap. Our lattice action is highly improved, with sources of discretization and finite volume errors systematically removed; we are able to demonstrate the expected volume scaling of energy levels of two and three untrapped fermions, and to reproduce the high precision calculations published previously for the ground state energies for N = 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3, . . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty). We use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64^3 x 72; our approach avoids the use of importance sampling or calculation of a fermion determinant and employs a novel statistical method for estimating observables, allowing us to generate ensembles as large as 10^8 while requiring only relatively modest computational resources.

hep-lat↗

arXiv2011

Noise, sign problems, and statistics

hep-lat↗