Entanglement spectra of critical and near-critical systems in one dimension

TL;DR

This paper investigates the entanglement spectra of one-dimensional critical and near-critical quantum systems using the iTEBD numerical method, confirming theoretical predictions and exploring the spectra's dependence on a single parameter.

Contribution

It demonstrates that the entanglement spectra of various 1D models align with theoretical predictions and confirms the iTEBD method's effectiveness in studying both integrable and non-integrable systems.

Findings

Eigenvalue distributions match Calabrese and Lefevre's approximation within a few percent.

Results validate the iTEBD approach against exact solutions for the transverse Ising model.

Entanglement spectra are governed by a single parameter across different models.

Abstract

The entanglement spectrum of a pure state of a bipartite system is the full set of eigenvalues of the reduced density matrix obtained from tracing out one part. Such spectra are known in several cases to contain important information beyond that in the entanglement entropy. This paper studies the entanglement spectrum for a variety of critical and near-critical quantum lattice models in one dimension, chiefly by the iTEBD numerical method, which enables both integrable and non-integrable models to be studied. We find that the distribution of eigenvalues in the entanglement spectra agrees with an approximate result derived by Calabrese and Lefevre to an accuracy of a few percent for all models studied. This result applies whether the correlation length is intrinsic or generated by the finite matrix size accessible in iTEBD. For the transverse Ising model, the known exact results for the entanglement spectrum are used to confirm the validity of the iTEBD approach. For more general models, no exact result is available but the iTEBD results directly test the hypothesis that all moments of the reduced density matrix are determined by a single parameter.