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The complete set of infinite volume ground states for Kitaev's abelian quantum double models

Cha, Matthew, Naaijkens, Pieter and Nachtergaele, Bruno 2018. The complete set of infinite volume ground states for Kitaev's abelian quantum double models. Communications in Mathematical Physics 357 (1) , pp. 125-157. 10.1007/s00220-017-2989-4

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Abstract

We study the set of infinite volume ground states of Kitaev’s quantum double model on Z 2 Z2 for an arbitrary finite abelian group G. It is known that these models have a unique frustration-free ground state. Here we drop the requirement of frustration freeness, and classify the full set of ground states. We show that the set of ground states decomposes into |G | 2 |G|2 different charged sectors, corresponding to the different types of abelian anyons (also known as superselection sectors). In particular, all pure ground states are equivalent to ground states that can be interpreted as describing a single excitation. Our proof proceeds by showing that each ground state can be obtained as the weak* limit of finite volume ground states of the quantum double model with suitable boundary terms. The boundary terms allow for states that represent a pair of excitations, with one excitation in the bulk and one pinned to the boundary, to be included in the ground state space.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Springer Verlag (Germany)
ISSN: 0010-3616
Date of First Compliant Deposit: 25 February 2020
Date of Acceptance: 18 December 2016
Last Modified: 07 Dec 2020 18:22
URI: http://orca.cf.ac.uk/id/eprint/129978

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