Entanglement structure of the Hubbard model in momentum space

G. Ehlers, J. Sólyom, O. Legeza, R. M. Noack

Research output: Article

13 Citations (Scopus)

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 U2 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.

Original languageEnglish
Article number235116
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume92
Issue number23
DOIs
Publication statusPublished - dec. 8 2015

Fingerprint

Hubbard model
Momentum
momentum
space density
Entropy
entropy
two dimensional models
Ground state
ground state
partitions
Numerical methods
Doping (additives)

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

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AU - Ehlers, G.

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AU - Legeza, O.

AU - Noack, R. M.

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N2 - 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 U2 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.

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