A simple fermionic model of deconfined phases and phase transitions

TL;DR

This paper uses Quantum Monte Carlo simulations to explore fermionic models with quantum Ising spins, revealing rich phase diagrams including deconfined phases, exotic phase transitions, and emergent gauge fields beyond traditional Landau-Ginzburg theory.

Contribution

It introduces a class of non-integrable fermionic models with emergent gauge fields and spontaneous symmetry breaking, expanding understanding of deconfined phases and unconventional phase transitions.

Findings

Identification of deconfined phases with gapless Dirac fermions and emergent $ ext{Z}_2$ gauge fields.

Observation of finite temperature phase transition associated with Gauss's law emergence.

Transitions from deconfined to short-range entangled phases, including Néel, superconductor, and VBS phases.

Abstract

Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with $N$ flavors of fermions per site for $N=1,2$ and $3$. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for $N>1$ corresponds to $2N$ gapless Dirac fermions coupled to an emergent $\mathbb{Z}_2$ gauge field in its deconfined phase. However, unlike a conventional $\mathbb{Z}_2$ gauge theory, we do not impose the `Gauss's Law' by hand and instead, it emerges due to spontaneous symmetry breaking. Correspondingly, unlike a conventional $\mathbb{Z}_2$ gauge theory in two spatial dimensions, our models have a finite temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short range entangled phase, which corresponds to N\'eel/Superconductor for $N=2$ and a Valence Bond Solid for $N=3$. Furthermore, for $N=3$, the Valence Bond Solid further undergoes a transition to a N\'eel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.