A classification of phases of bosonic quantum lattice systems in one dimension
Abstract
We study invertible states of 1d bosonic quantum lattice systems. We show that every invertible 1d state is in a trivial phase: after tensoring with some unentangled ancillas it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G the only obstruction is an index valued in degree-2 cohomology of . We show that two invertible -invariant states are in the same phase if and only if their indices coincide.
Keywords
Cite
@article{arxiv.2012.15491,
title = {A classification of phases of bosonic quantum lattice systems in one dimension},
author = {Anton Kapustin and Nikita Sopenko and Bowen Yang},
journal= {arXiv preprint arXiv:2012.15491},
year = {2021}
}
Comments
Errors in the proofs of Lemma 4.5 and Theorem 1 have been corrected. The new version also includes an appendix on a multiplicative version of the Lieb-Robinson bound