Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions

TL;DR

This paper studies quantum phase transitions in 2+1D U(1) gauge theories with fermions and bosons, calculating critical exponents and universal amplitudes relevant for quantum magnets and spin liquids.

Contribution

It provides large-N computations of critical properties for U(1) gauge theories with mixed matter content, connecting to experimental and numerical studies of quantum magnets.

Findings

Computed critical exponents for various N_b/N_f ratios

Derived universal amplitudes for the conformal field theories

Linked theoretical results to experimental observables in quantum magnets

Abstract

We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b species of complex bosons and N_f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large N_b and N_f, but for arbitrary values of the ratio N_b/N_f, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin-liquids, charge-liquids and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.