Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions

TL;DR

This paper demonstrates that the 2+1D U(1) spin liquid with a spinon Fermi surface remains stable against instanton proliferation, supporting the validity of the non-compact U(1) gauge theory as a low-energy effective description.

Contribution

It introduces a mapping of the spinon Fermi surface to 1+1D chiral fermions, showing instantons have infinite scaling dimension, thus establishing stability.

Findings

Spin liquid phase is stable against instantons.

Non-compact U(1) gauge theory accurately describes the low-energy physics.

Instantons are irrelevant due to infinite scaling dimension.

Abstract

We study the stability of the 2+1 dimensional U(1) spin liquid state against proliferation of instantons in the presence of spinon Fermi surface. By mapping the spinon Fermi surface into an infinite set of 1+1 dimensional chiral fermions, it is argued that an instanton has an infinite scaling dimension for any nonzero number of spinon flavors. Therefore, the spin liquid phase is stable against instantons and the non-compact U(1) gauge theory is a good low energy description.