Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases

TL;DR

This study uses sign-problem-free quantum Monte Carlo simulations to explore the phase diagram of lattice compact QED with fermionic matter in 2+1 dimensions, revealing various confined and deconfined quantum phases and transitions.

Contribution

It demonstrates the feasibility of simulating compact U(1) lattice gauge theories with fermions without sign problems, mapping out phase diagrams and identifying quantum critical points.

Findings

Deconfined phases with algebraic correlations observed.

Continuous quantum phase transition between VBS and Néel order at four flavors.

Emergence of various confined phases with spontaneous symmetry breaking.

Abstract

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and N\'eel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f = 4$, our data suggests a continuous quantum phase transition between the VBS and N\'{e}el order. We also provide preliminary theoretical analysis for these quantum phase transitions.