A classification of phases of bosonic quantum lattice systems in one dimension

• URL: http://arxiv.org/abs/2012.15491v6
• Date: Thu, 9 Dec 2021 06:30:55 GMT
• Title: A classification of phases of bosonic quantum lattice systems in one dimension
• Authors: Anton Kapustin, Nikita Sopenko, Bowen Yang
• Abstract summary: We study invertible states of 1d bosonic quantum lattice systems. We show that every invertible 1d state is in a trivial phase. We show that two invertible $G$-invariant states are in the same phase if and only if their indices coincide.
• Score: 10.495593679303031
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $G$. We show that two invertible $G$-invariant states are in the same phase if and only if their indices coincide.

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