Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes

TL;DR

This paper investigates (3+1)-dimensional quantum link models, including fermionic variants, using large-scale exact diagonalization, revealing a proposed Coulomb phase and differences between bosonic and fermionic spectra.

Contribution

It introduces fermionic quantum links in (3+1)d models and compares their spectra to bosonic models, highlighting key differences and proposing experimental realizations.

Findings

Proposed the existence of a Coulomb phase in (3+1)d U(1) lattice gauge theory.

Established spectral equivalence in (2+1)d but differences in (3+1)d between bosonic and fermionic models.

Discussed experimental prospects for realizing magnetic field interactions in quantum simulators.

Abstract

Quantum link models (QLMs) have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories (LGT), and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this article, we study the Abelian $U(1)$ lattice gauge theory in $(3+1)$-d tubes using large-scale exact diagonalization (ED). We are then able to motivate the phase diagram of the model with finite size scaling techniques (FSS), and in particular propose the existence of a Coulomb phase. Furthermore, we introduce the first models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the $U(1)$-symmetric quantum link models in $(2+1)$-d, they are different in $(3+1)$-d. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.