Robust Fermi-Liquid Instabilities in Sign Problem-Free Models.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Computational Physics

Background:

• Determinant quantum Monte Carlo (DQMC) is a key numerical method for studying fermionic systems.
• Sign-free (SF) models offer a way to bypass the fermion sign problem, a major hurdle in DQMC.
• The physical limitations and accessible quantum phases of SF models remain poorly understood.

Purpose of the Study:

• To investigate the inherent physical characteristics and limitations of sign-free models in DQMC.
• To determine which zero-temperature quantum phases are accessible or fundamentally inaccessible in SF models.
• To explore the relationship between Fermi liquids and the fermion sign problem.

Main Methods:

• Analysis of known sign-free model classes within determinant quantum Monte Carlo.
• Investigation of symmetry properties, including antiunitary and nonunitary symmetries.
• Examination of the stability of ground states and fixed points, particularly Fermi liquid states.
• Study of Fermi surface stability at the quadratic action level for lower-symmetry SF models.

Main Results:

• Models in known SF classes cannot possess stable Fermi-liquid ground states in d≥2 dimensions without spontaneous symmetry breaking.
• For symmetry-class SF models, attractive Cooper-like interactions destabilize Fermi liquid fixed points.
• In lower-symmetry SF models, Fermi surfaces are generically unstable even at the quadratic action level.
• A fundamental link between Fermi liquids and the fermion sign problem is suggested.

Conclusions:

• Sign-free models present fundamental limitations regarding stable Fermi-liquid ground states.
• The absence of the sign problem in SF models restricts the types of quantum phases that can be realized.
• Non-Fermi-liquid ground states with Fermi surfaces may still be accessible in sign-free models.