Robust Fermi liquid instabilities in sign problem-free models

TL;DR

This paper demonstrates that sign-problem-free fermionic models in two or more dimensions cannot host stable Fermi liquids unless certain symmetries are broken, revealing fundamental limitations of these models and linking the sign problem to Fermi liquid stability.

Contribution

It establishes that known sign-free models cannot sustain stable Fermi liquids in higher dimensions without symmetry breaking, highlighting inherent physical constraints of such models.

Findings

Sign-free models in d≥2 cannot have stable Fermi liquids without symmetry breaking.

Fermi surfaces in these models are generically unstable at the quadratic level.

Non-Fermi liquid states with Fermi surfaces are not ruled out in sign-free models.

Abstract

Determinant Quantum Monte Carlo (DQMC) is a powerful numerical technique to study many-body fermionic systems. In recent years, several classes of sign-free (SF) models have been discovered, where the notorious sign problem can be circumvented. However, it is not clear what are the inherent physical characteristics and limitations of SF models. In particular, which zero-temperature quantum phases of matter are accessible within such models, and which are fundamentally inaccessible? Here, we show that a model belonging to any of the known SF classes within DQMC cannot have a stable Fermi liquid ground state in spatial dimension $d\ge 2$, unless the anti-unitary symmetry that prevents the sign problem is spontaneously broken (for which there are currently no known examples in SF models). For SF models belonging to one of the symmetry classes (where the absence of the sign problem follows from a combination of non-unitary symmetries of the fermionic action), any putative Fermi liquid fixed point generically includes an attractive Cooper-like interaction that destabilizes it. In the recently discovered lower-symmetry classes of SF models, the Fermi surface is generically unstable even at the level of the quadratic action. Our results suggest a fundamental link between Fermi liquids and the fermion sign problem. Interestingly, our results do not rule out a non-Fermi liquid ground state with a Fermi surface in a sign-free model.