A Commuting Projector Model with a Non-zero Quantized Hall conductance

Autor:	DeMarco, Michael, Wen, Xiao-Gang
Rok vydání:	2021
Předmět:	Condensed Matter - Strongly Correlated Electrons High Energy Physics - Lattice
Druh dokumentu:	Working Paper
Popis:	By ungauging a recently discovered lattice rotor model for Chern-Simons theory, we create an exactly soluble path integral on spacetime lattice for $U^\kappa(1)$ Symmetry Protected Topological (SPT) phases in $2+1$ dimensions with a non-zero Hall conductance. We then convert the path integral on a $2+1$d spacetime lattice into a $2$d Hamiltonian lattice model, and show that the Hamiltonian consists of mutually commuting local projectors. We confirm the non-zero Hall conductance by calculating the Chern number of the exact ground state. It has recently been suggested that no commuting projector model can host a nonzero Hall conductance. We evade this no-go theorem by considering a rotor model, with a countably infinite number of states per site. Comment: 4 pages, 2 figures, and Appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.13057 Zobrazit plný text záznamu View this record from Arxiv