Demonstration of a fermion Quadrupling Condensate via Quantum Monte Carlo Simulation

TL;DR

This paper presents a microscopic fermionic model with correlated hopping that enables Monte Carlo simulations, providing evidence for a fermion quadrupling condensate and its potential realization in ultracold gases.

Contribution

It introduces a new fermionic model that reduces the sign problem, allowing the first rigorous numerical demonstration of a fermion quadrupling condensate.

Findings

Demonstrates existence of a fermion-quadrupling condensate in the model.

Shows the transition temperature is comparable to the hopping energy scale.

Provides evidence that such exotic states are experimentally accessible.

Abstract

Fermionic condensation typically occurs via pairing. In recent decades, however, a fundamental question has emerged: whether alternative forms of order exist, such as condensates of fermion quadruplets. These states--including ``charge-4e" superconductors and ``charge-0" counterflow condensates--lie beyond the standard Bardeen-Cooper-Schrieffer framework, and require strong fluctuations and correlation effects that invalidate the BCS mean-field description. This makes the problem notoriously difficult to study numerically at a microscopic level, as it involves both strong interactions and the fermionic sign problem. Here, we present a microscopic fermionic model featuring correlated hopping that significantly mitigates the sign problem, enabling rigorous Monte-Carlo-based analysis. Using large-scale simulations, we demonstrate the existence of a fermion-quadrupling condensate with a transition temperature comparable to the hopping energy scale. These results provide direct numerical evidence for quartic fermionic order in a microscopic system and suggest that these exotic states are also experimentally accessible in ultracold atomic gases.