A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions

Autor:	Nussinov, Zohar, Ortiz, Gerardo
Rok vydání:	2022
Předmět:	Quantum Physics Condensed Matter - Statistical Mechanics Condensed Matter - Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevB.107.045109
Popis:	We establish, in the spirit of the Lieb-Schultz-Mattis theorem, lower bounds on the spectral degeneracy of quantum systems with higher (Gauge Like) symmetries with rather generic physical boundary conditions in an arbitrary number of spatial dimensions. Contrary to applying twists or equivalent adiabatic operations, we exploit the effects of modified boundary conditions. When a general choice of boundary geometry is immaterial in approaching the thermodynamic limit, systems that exhibit non-commuting Gauge Like symmetries, such as the orbital compass model, must have an exponential (in the size of the boundary) degeneracy of each of their spectral levels. We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors, i.e., of those of systems with non-extensive degeneracies, due to entropic "order by disorder" type effects. Comment: 21 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.11690 Zobrazit plný text záznamu View this record from Arxiv