Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids

TL;DR

This paper uses renormalization group analysis to determine the conditions under which deconfinement occurs in 2+1D quantum electrodynamics, showing the stability of spin liquids for certain fermion numbers.

Contribution

It provides a detailed RG analysis revealing the critical fermion number for deconfinement and the stability of U(1) spin liquids in 2+1D QED.

Findings

Deconfinement occurs for N > 1.161.

A universal jump in string tension at N_c.

Stability of spin liquids at N=2.

Abstract

Compact quantum electrodynamics in 2+1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when $N>N_c=36/\pi^3\approx 1.161$, where $N$ is the number of fermion replica. For $N<N_c$, however, there are two stable fixed points separated by a line containing a unstable non-trivial fixed point: a fixed point corresponding to the scaling limit of the non-compact theory, and another one governing the scaling behavior of the compact theory. The string tension associated to the confining interspinon potential is shown to exhibit a universal jump as $N\to N_c^-$. Our results imply the stability of a spin liquid at the physical value N=2 for Mott insulators.