Introducing Fermionic Link Models

TL;DR

This paper investigates $U(1)$ quantum link models using bosonic and fermionic representations, revealing identical physics in 2D but different phase behaviors in 3D, including quantum phase transitions and multiple phases.

Contribution

It introduces a fermionic representation of quantum link models and compares their phase structures with bosonic models in 2D and 3D.

Findings

Bosonic and fermionic QLMs show identical physics in 2D.

In 3D, bosonic QLMs exhibit a quantum phase transition to a spin liquid.

Fermionic QLMs display two distinct phases beyond symmetry breaking.

Abstract

Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of $U(1)$ symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs display the same physics. We then explore the models in 3D and find different behavior for the two QLMs. For the bosons, we see evidence for a quantum phase transition from a symmetry broken phase to a potential quantum spin liquid phase. For the fermions, we identify not one but two distinct phases in addition to a symmetry broken phase. We explore the symmetries of the ground state in the strong coupling limit, which breaks lattice symmetries and examine the spectrum for both models.