Exact Entanglement Studies of Strongly Correlated Systems: Role of Long-Range Interactions and Symmetries of the System

TL;DR

This paper investigates how long-range interactions and symmetries influence bipartite entanglement in strongly correlated systems, explaining the effectiveness of DMRG and revealing entanglement behavior across energy states.

Contribution

It provides a detailed analysis of entanglement in models with long-range interactions and explores the role of symmetries, enhancing understanding of DMRG applicability and entanglement profiles.

Findings

Long-range interactions affect entanglement spectra significantly.

Symmetry properties influence entanglement characteristics.

Entanglement profiles vary across energy states and relate to density of states.

Abstract

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.