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arXiv:1503.00296 · Physica B Condensed Matter

Physical structure of point-like interactions for one-dimensional Schrödinger operator and the gauge symmetry

В. Л. Кулинский, D. Yu. Panchenko

Published May 18, 2015• 21 citations
arXivHTMLPDF
DOI
10.1016/j.physb.2015.05.011

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We demonstrate that in the scaling limit the phenomenon of spin-charge separation as encountered in Luttinger liquids defined on the lattice can be associated with the emergence of local Ising symmetry. This Z_2 gauge field is of geometrical nature (sublattice parity) and the Luttinger liquid corresponds with the critical point where the symmetry is on the verge of becoming local. We argue that in a true one dimensional superconductor the local symmetry will be fully realized as long as the geometrical structure associated with spin-charge separation is maintained.
Spatially modulated symmetries have emerged since the discovery of fractons, which characterize unconventional topological phases with mobility-constrained quasiparticle excitations. On the other hand, noninvertible symmetry operators have attracted substantial attention in communities of high energy and condensed matter physics due to their deep insight into quantum anomalies and exotic phases of matter. However, the connection between these exotic and noninvertible symmetries has not been fully explored. In this paper, we construct concrete lattice models with noninvertible symmetry operators via gauging spatially modulated symmetries and investigate their exotic fusion rules. Specifically, we construct spin models with subsystem symmetries or dipole symmetries on one, two, and three-dimensional lattices. Gauging subsystem symmetries leads to noninvertible symmetry operators whose fusion rules involve 0-form subsystem charges in two dimensions and higher-form operators that correspond to ``lineon'' excitations (excitations which are mobile along one-dimensional line) in three dimensions. Gauging dipole symmetries leads to noninvertible symmetry operators with dipole algebras that describe a hierarchical structure between global and dipole charges. Notably, the hierarchical structure of the dual dipole charges is inverted compared with the original ones. Our work provides a unified and systematic analytical framework for constructing exotic symmetry operators by gauging relevant symmetries.