CJTCS Volume 2016 Article 9

Volume 2016

Article 9

Published by the Department of Computer Science, The University of Chicago.

Computing the Degenerate Ground Space of Gapped Spin Chains in Polynomial Time

Christopher T. Chubb
University of Sydney,
Sydney, NSW, Australia;
christopher DOT chubb AT sydney DOT edu DOT au

Steven T. Flammia
University of Sydney,
Sydney, NSW, Australia;
steven DOT flammia sydney DOT edu DOT au

July 27, 2016

Abstract

Given a gapped Hamiltonian of a spin chain, we give a polynomial-time algorithm for finding the degenerate ground space projector. The output is an orthonormal set of matrix product states that approximate the true ground space projector up to an inverse polynomial error in any Schatten norm, with a runtime exponential in the degeneracy. Our algorithm is an extension of the recent algorithm of Landau, Vazirani, and Vidick for the nondegenerate case, and it includes the recent improvements due to Huang. The main new idea is to incorporate the local distinguishability of ground states on the half-chain to ensure that the algorithm returns a complete set of global ground states.

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Submitted June 16, 2015, revised May 12, 2016, and in final form July 24, 2016, published July 27, 2016.

DOI: 10.4086/cjtcs.2016.009