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

Kapustin, Anton and Sopenko, Nikita and Yang, Bowen (2020) A classification of phases of bosonic quantum lattice systems in one dimension. . (Unpublished)

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We study the entanglement properties of quantum phases of bosonic 1d lattice systems in infinite volume. We show that a ground state of any gapped local Hamiltonian is Short-Range Entangled: it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. We characterize Short-Range Entangled states in terms of decay properties of their Schmidt coefficients. If a Short-Range Entangled state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries. We show that in the case of a finite unitary symmetry G the only obstruction for the existence of a symmetry-preserving disentangler is an index valued in degree-2 cohomology of G. We show that two Short-Range Entangled states are in the same phase if and only if their indices coincide.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Sopenko, Nikita0000-0002-8479-1924
Record Number:CaltechAUTHORS:20210301-154744254
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108260
Deposited By: Tony Diaz
Deposited On:02 Mar 2021 00:24
Last Modified:02 Mar 2021 00:24

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