Improved lattice operators for nonrelativistic fermions

Abstract

In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite latticespacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I construct, in particular, highly improved representations for the energy and the contact as a first step in an improvement program for finite-temperature calculations. I illustrate the effects of improvement on those quantities with a ground-state lattice calculation at unitarity.

Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

“…However, a better route may be the use of improved actions and operators (see, e.g., Ref. [23]) to reduce lattice spacing effects at fixed volume.…”

“…We employed the same technique as in Refs. [23] adapted to one dimensions. Following that approach, we placed our system in a Euclidean spacetime lattice of extent N x × N τ and used a Trotter-Suzuki decomposition of the Boltzmann weight followed by a Hubbard-Stratonovich transformation [24].…”

Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices and particle-partition entanglement

“…For our ground-state calculations, we employ the techniques previously used in Refs. [10,30,31]. Specifically, we formulate the given quantum many-body problem on a discretized Euclidean spacetime of dimensionless extent N x × N τ .…”

Finite-Temperature Equation of State of Polarized Fermions at Unitarity

“…Thus, the computational challenge, besides the sign problem, is that of opening that window of scales by making N x and β as large as possible, in that order, and staying in a dilute regime to suppress artifacts associated with the ultraviolet energy cutoff imposed by the lattice. Note that the reliability of calculations based on our present set of spacetime lattice parameters has been analyzed in detail in the past [74][75][76][77][78][79].…”