Linear Canonical-Ensemble Quantum Monte Carlo: From Dilute Fermi Gas to Flat-Band Ferromagnetism

TL;DR

This paper introduces a new quantum Monte Carlo algorithm that enforces exact fermion number, significantly speeds up simulations of dilute fermionic systems, and uncovers ferromagnetic behavior in flat-band models.

Contribution

The authors develop a stabilized QR update that reduces computational complexity, enabling large-scale, unbiased simulations of dilute correlated fermions with exact particle number control.

Findings

Speedup in dilute regimes ($N_e \\ll N$) due to linear scaling algorithm.

Observation of fermion sign problem suppression in dilute Fermi gas.

Detection of ferromagnetic instability at low temperatures in flat-band systems.

Abstract

We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces the computational complexity from standard cubic scaling $O(\beta N^3)$ to linear scaling $O(\beta N N_e^2)$ with respect to the system size $N$, where $N_e$ is the particle number. This yields a dramatic speedup in dilute regimes ($N_e \ll N$), opening unbiased access to large-scale simulations of strongly correlated low-density phases. We validate the method on the dilute Fermi gas with onsite Hubbard interactions, observing the suppression of the fermion sign problem in the dilute limit. Furthermore, we apply this approach to an one-dimensional flat-band system, where the canonical ensemble allows for precise control over filling. We reveal a ferromagnetic instability at low temperatures in the half-filling regime. Our linear-scaling approach provides a powerful tool for investigating emergent phenomena in dilute quantum matter.