Semidefinite Programs at Finite Fermion Density

TL;DR

This paper explores the use of semidefinite programming to analyze finite-density fermionic quantum systems, demonstrating that it can bypass traditional sign problem issues in lattice models.

Contribution

It shows that semidefinite programs remain effective for finite-density fermionic theories, avoiding the sign problem that hampers other computational methods.

Findings

Semidefinite programs accurately analyze finite-density fermionic models.

No sign problem-related difficulties observed in the Thirring model.

Potential for non-perturbative analysis of quantum systems at finite density.

Abstract

Semidefinite programs can be constructed to provide a non-perturbative view of the zero-temperature behavior of quantum systems. This paper examines the properties of these semidefinite programs when applied to lattice-regulated field theories exhibiting fermion sign problems. Specifically on the finite-density Thirring model, there is no indication that the accuracy of semidefinite programs suffers from any difficulty analogous to the sign problem.