Entanglement structure of the Hubbard model in momentum space

TL;DR

This paper investigates the entanglement properties of the ground states of the Hubbard model in momentum space using numerical methods, revealing how entanglement measures vary with interaction strength and system size.

Contribution

It introduces a momentum-space entanglement analysis of the Hubbard model and demonstrates the effectiveness of momentum-space DMRG for weak coupling regimes.

Findings

Subsystem entropy scales with $U^2$ at weak coupling

Entanglement measures provide insights into ground state nature

Momentum-space DMRG yields accurate results at moderate sizes

Abstract

We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix renormalization group (DMRG). In particular, we investigate quantities such as the single-site entropy and two-site mutual information of single-particle momentum states as well as the behavior of the bipartite subsystem entropy for partitions in momentum space. The distribution of these quantities in momentum space gives insight into the fundamental nature of the ground state, insight that can be used to make contact with weak-coupling-based analytic approaches and to optimize numerical methods, the momentum-space DMRG in particular. We study the site and subsystem entropies as a function of interaction strength $U$ and system size. In both the one- and two-dimensional cases, we find that the subsystem entropy scales proportionally to $U^2$ for weak $U$ and proportionally to volume. Nevertheless, the optimized momentum-space DMRG can provide variationally accurate results for the two-dimensional Hubbard model at weak coupling for moderate system sizes.