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

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.

33 pages

References in corpus (7)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix product states represent ground states faithfully
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Stochastic Error Cancellation in Analog Quantum Simulation
• Area law in one dimension: Degenerate ground states and Renyi entanglement entropy
• The Detectability Lemma and Quantum Gap Amplification

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