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Monopoles in Dirac spin liquids and their symmetries from instanton calculus
by Shankar Ganesh, Joseph Maciejko
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | G. Shankar |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2310.06748v2 (pdf) |
| Date accepted: | 2024-04-10 |
| Date submitted: | 2024-03-12 18:17 |
| Submitted by: | Shankar, G. |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
We hereby resubmit our manuscript, with revisions based on the suggestions and comments by the referees in their reports. In addition, we have also submitted responses to the questions raised in these reports.
Sincerely,
G. Shankar and Joseph Maciejko
List of changes
1. A new paragraph has been added on page 6 below equation (11), on the generality of the spinon mass terms considered.
2. A discussion of the validity of the dilute gas approximation appears below equation (13) on page 7.
3. The caption for figure 1 on page 9 has been extended.
4. Typographical and grammatical errors have been corrected.
Published as SciPost Phys. 16, 118 (2024)