2023
DOI: 10.1007/jhep05(2023)017
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Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Abstract: We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,…). These lattice models therefore ha… Show more

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Cited by 11 publications
(3 citation statements)
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“…(94) 19 After the completion of this work the papers [52,53] discussed Hamiltonian formulations of various modified Villain models. 20 This model is usually introduced in solid state physics as a simple model for phonons, where φ j is the displacement of an atom at site j from the lattice position.…”
Section: The System and Its Symmetriesmentioning
confidence: 99%
“…(94) 19 After the completion of this work the papers [52,53] discussed Hamiltonian formulations of various modified Villain models. 20 This model is usually introduced in solid state physics as a simple model for phonons, where φ j is the displacement of an atom at site j from the lattice position.…”
Section: The System and Its Symmetriesmentioning
confidence: 99%
“…45 It would also be interesting to realize non-invertible symmetries in the Hamiltonian formalism of the modified Villain lattice model [52,151]. 46 See [13] and Appendix C for an alternative construction of the defect Hamiltonian for D of the critical transverse-field Ising model from bosonization of the Majorana chain on odd number of sites.…”
Section: B2 the Non-invertible Defect D From Gauging In Half Of Spacementioning
confidence: 99%
“…Here we discuss the modified Villain model of compact boson theory [119][120][121], which realizes anomalous chiral U(1) L and U(1) R symmetries of the compact boson theory on the lattice. We study the Hamiltonian description of this model that was presented in [57,122]. At the end of this section, we explain how to construct Abelian chiral gauge theories on the lattice using the modified Villain theory.…”
Section: Lattice Chiral Gauge Theories -The Modified Villain Modelmentioning
confidence: 99%