Entanglement renormalization for disordered systems

TL;DR

This paper introduces a tensor network method based on entanglement renormalization and strong disorder renormalization group techniques to efficiently study ground states of strongly disordered one-dimensional quantum systems.

Contribution

It presents a novel tensor network ansatz tailored for disordered systems, combining entanglement renormalization with strong disorder renormalization group insights.

Findings

Accurately captures ground state entanglement at long distances

Provides an efficiently contractible tensor network for 1D disordered systems

Generalizes the multi-scale entanglement renormalization ansatz for disorder

Abstract

We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered XXZ model demonstrates that this approach accurately captures ground state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for 1D systems, which may be understood as a generalization of the multi-scale entanglement renormalization ansatz for disordered systems.