Algorithms for the Markov Entropy Decomposition

Abstract

The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the MED is both more accurate and significantly more flexible.

12 pages, 9 figures

References in corpus (3)

• N-representability is QMA-complete
• Quantum Graphical Models and Belief Propagation
• Quantum Belief Propagation

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• Fermionic Projected Entangled Pair States at Finite Temperature
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