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 $G$. We show that two invertible $G$-invariant states are in the same phase if and only if their indices coincide.

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

References in corpus (2)

• Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
• The classification of symmetry protected topological phases of one-dimensional fermion systems

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• The index of a pair of pure states and the interacting integer quantum Hall effect