Tree tensor networks and entanglement spectra

TL;DR

This paper introduces a tree tensor network variational method for simulating quantum many-body systems with symmetries, and provides a scheme to extract entanglement spectra across bipartitions, revealing boundary effects.

Contribution

It presents a novel tensor network approach that simplifies optimization via charge configurations and a method to compute entanglement spectra in loopless networks.

Findings

Entanglement spectra depend on subsystem boundaries.

Method successfully applied to 2xL, 3xL, 4xL systems.

Boundary conditions influence entanglement properties.

Abstract

A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the entanglement spectra in a bipartite splitting of a loopless tensor network across multiple links of the network, by constructing a matrix product operator for the reduced density operator and simulating its eigenstates. The entanglement spectra of 2 x L, 3 x L and 4 x L with either open or periodic boundary conditions on the rungs are studied using the presented methods, where it is found that the entanglement spectrum depends not only on the subsystem but also on the boundaries between the subsystems.