Projected Entangled Pair States with flexible geometry

TL;DR

This paper introduces a flexible PEPS algorithm that adapts to arbitrary and fluctuating graph geometries, enabling efficient simulation of complex quantum many-body systems with dense and irregular connections.

Contribution

The authors develop a PEPS method with a tunable vertex degree constraint, allowing dynamic adaptation to system geometry and broadening tensor network applications.

Findings

Successfully simulated classical spin glasses and quantum annealing on dense graphs.

Demonstrated the impact of the vertex degree cutoff on simulation accuracy.

Extended PEPS applicability to irregular and fluctuating geometries.

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, $\kappa \in \mathbb{N}$, 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 $\kappa$ when simulating a uniform quantum spin model on a regular (square) lattice. Our work opens the way to apply tensor network algorithms to arbitrary, even fluctuating, background geometries.