Monopoles in Dirac spin liquids and their symmetries from instanton calculus

TL;DR

This paper develops a semiclassical instanton approach to construct and analyze monopole operators in Dirac spin liquids, revealing their quantum numbers and symmetry properties without relying on conformal invariance.

Contribution

It introduces a direct instanton-based method to determine monopole operators and their quantum numbers in 2D Dirac spin liquids, complementing previous conformal field theory approaches.

Findings

Constructed monopole operators using instanton calculus.

Determined monopole quantum numbers on bipartite lattices.

Resummation of instanton gas selects the relevant monopole for proliferation.

Abstract

The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact $U(1)$ gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced 't Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.