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Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
by Urban F. P. Seifert, Sergej Moroz
Submission summary
| Authors (as registered SciPost users): | Sergej Moroz · Urban Seifert |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2306.09405v3 (pdf) |
| Date accepted: | 2024-05-13 |
| Date submitted: | 2024-05-03 13:50 |
| Submitted by: | Seifert, Urban |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Emergent gauge theories take a prominent role in the description of quantum matter, supporting deconfined phases with topological order and fractionalized excitations. A common construction of $\mathbb{Z}_2$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links and subject to a discrete $\mathbb{Z}_2$ Gauss law constraint. As shown by Kitaev, $\mathbb{Z}_2$ lattice gauge theories also emerge in the exact solution of certain spin systems with bond-dependent interactions. In this context, the $\mathbb{Z}_2$ gauge field is constructed from Majorana fermions, with gauge constraints given by the parity of Majorana fermions on each site. In this work, we provide an explicit Jordan-Wigner transformation that maps between these two formulations on the square lattice, where the Kitaev-type gauge theory emerges as the exact solution of a spin-orbital (Kugel-Khomskii) Hamiltonian. We then apply our mapping to study local perturbations to the spin-orbital Hamiltonian, which correspond to anisotropic interactions between electric-field variables in the $\mathbb{Z}_2$ gauge theory. These are shown to induce anisotropic confinement that is characterized by emergence of weakly-coupled one-dimensional spin chains. We study the nature of these phases and corresponding confinement transitions in both absence and presence of itinerant fermionic matter degrees of freedom. Finally, we discuss how our mapping can be applied to the Kitaev spin-1/2 model on the honeycomb lattice.
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- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
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Author comments upon resubmission
We are grateful for the Referees' careful reading of our manuscript and their constructive comments. We are happy that their overall assessment of our work has been positive. We address their individual comments/concerns by replying to their reports, and provide a list of changes with our resubmission.
We hope that our resubmitted manuscript can be accepted for publication in SciPost in the present form.
Best regards,
Urban Seifert and Sergej Moroz
List of changes
Major changes to the text and content are marked in blue.
- Added a number of references, in particular including Refs. 20, 22, 33, 34, 47-65.
- In Sec. 3.1.1: Discussion on deriving expressions of gauge-invariant lattice gauge theory operators \sigma^x_{i,j} and \sigma^y_{i,j} in terms of spin-orbital operators, and vice versa.
- In Sec. 4.1: Added sentences that references Sec. 3.1.1.
- In Sec. 5: Added outlook/suggestions for studying deconfinement and Higgs transitions within a continuum critical field theory
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)