From Popov-Fedotov trick to universal fermionization

TL;DR

This paper generalizes the Popov-Fedotov fermionization trick to a broader class of quantum systems, enabling more efficient diagrammatic Monte Carlo simulations by transforming complex many-body interactions into simpler single-particle energies.

Contribution

It extends the Popov-Fedotov method to bosons with fixed occupation limits and fermionic Hamiltonians with constraints, introducing a versatile fermionization approach for improved computational techniques.

Findings

Generalized fermionization to bosons and constrained fermionic systems.

Converted many-body couplings into single-particle energies.

Enhanced the efficiency and convergence of diagrammatic Monte Carlo methods.

Abstract

We show that Popov-Fedotov trick of mapping spin-1/2 lattice systems on two-component fermions with imaginary chemical potential readily generalizes to bosons with a fixed (but not limited) maximal site occupation number, as well as to fermionic Hamiltonians with various constraints on the site Fock states. In a general case, the mapping---fermionization---is on multi-component fermions with many-body non-Hermitian interactions. Additionally, the fermionization approach allows one to convert large many-body couplings into single-particle energies, rendering the diagrammatic series free of large expansion parameters; the latter is essential for the efficiency and convergence of the diagrammatic Monte Carlo method.