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  • Letter
  • Open Access

Projected entangled pair states with flexible geometry

Siddhartha Patra1,2, Sukhbinder Singh3, and Román Orús1,2,4

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Phys. Rev. Research 7, L012002 – Published 6 January, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012002

Abstract

Projected entangled pair states (PEPS) are a class of quantum many-body states that generalize matrix product states for one-dimensional systems to higher dimensions. In recent years, PEPS have advanced understanding of strongly correlated systems, especially in two dimensions, e.g., quantum spin liquids. Typically described by tensor networks on regular lattices (e.g., square, cubic), PEPS have also been adapted for irregular graphs; however, the computational cost becomes prohibitive for dense graphs with large vertex degrees. In this paper, we present a PEPS algorithm to simulate low-energy states and dynamics defined on arbitrary, fluctuating, and densely connected graphs. We introduce a cut-off, κ∈N, to constrain the vertex degree of the PEPS to a set but tunable value, which is enforced in the optimization by applying a simple edge-deletion rule, allowing the geometry of the PEPS to change and adapt dynamically to the system's correlation structure. We benchmark our flexible PEPS algorithm with simulations of classical spin glasses and quantum annealing on densely connected graphs with hundreds of spins, and also study the impact of tuning κ when simulating a uniform quantum spin model on a regular (square) lattice. Our paper opens the way to apply tensor network algorithms to arbitrary, even fluctuating, background geometries.

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References (30)

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Phys. Rev. Research 7, L012002– Published 6 January, 2025
  • Received 9 August 2024
  • Accepted 11 December 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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