Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Entanglement and position-space information entropy: Hubbard model as an approximation to nanostructure systems

J. P. Coe, V. V. França, Irene D’Amico

Published Jul 6, 2011• 1 citation
Publisher

Abstract

We consider the position-space information and linear entropies as proxy measures to the average single-site entanglement–quantified using the von Neumann entropy–of the one-dimensional Hubbard model and of a one-dimensional nanostructure system comprised of an array of quantum-dots. Spatial entanglement in the quantum-dot system is also investigated via the three entropies. We appraise the use of the possible proxy measures in the Hubbard model as an approximation to their use for the nanostructure system.

DOI
10.1088/1742-6596/303/1/012110

Related papers

Approximation of the entanglement in quantum dot chains using Hubbard models

J. P. Coe, V. V. França, Irene D’Amico

We investigate the Hubbard model, and the extended Hubbard model with and without correlated hopping, as an approximation to the average single-site (or local) entanglement of two-electron one-dimensional quantum dot chains with long range interactions. We focus on the effect of the chain length on the approximation accuracy. We also consider the particle-particle spatial entanglement of the three Hubbard models using the technique of Ref. [3] and compare the accuracy of this approximation to the numerically exact results of the nanostructure system.

Journal of Physics Conference Series•Mar 1, 2011•3 citations

Hubbard model as an approximation to the entanglement in nanostructures

J. P. Coe, V. V. França, Irene D’Amico

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in $M$ wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement.

arXiv:1003.3562•Physical Review A•May 17, 2010•31 citations

Geometry induced entanglement transitions in nanostructures

J. P. Coe, S. Abdullah, Irene D’Amico

We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.

arXiv:1003.3781•Journal of Applied Physics•Apr 21, 2010•3 citations

Quasilocal entanglement across the Mott-Hubbard transition

Gabriele Bellomia, Carlos Mejuto-Zaera, Massimo Capone +1 more

The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work, we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the intersite distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the $2d$ Hubbard model.

arXiv:2308.13706•Physical review. B./Physical review. B•Mar 4, 2024•16 citations

Single-site entanglement as a marker for quantum phase transitions at nonzero temperatures

Willdauany C. de Freitas da Silva, Andressa R. Medeiros-Silva, Rubem Mondaini +2 more

Entanglement has been widely investigated in condensed-matter systems since they are considered good candidates for developing quantum technologies. Additionally, entanglement is a powerful tool to explore quantum phase transitions in strongly correlated systems, with the von Neumann entropy being considered a proper measure of quantum entanglement for pure bipartite systems. For lattice systems, in particular, the single-site entanglement quantifies how much information about the quantum state of the remaining sites can be obtained by a measurement at a single site. Here, we use quantum Monte Carlo calculations to obtain the average single-site entanglement for the two-dimensional Hubbard model in different geometries, probing the effects of varying temperature and interaction strength. We find that the average single-site entanglement signals the quantum phase transitions in such systems, allowing us to identify and characterize signatures of quantum phase transitions even at finite temperatures. We also analyze the relation between entanglement and magnetic susceptibility: in all the geometries considered, we find regimes in which the quantities are roughly linearly connected, revealing their link to the Mott transition.

Physical Review A•Nov 21, 2025•0 citations

Entanglement structure of the Hubbard model in momentum space

G. Ehlers, Jenő Sólyom, Örs Legeza +1 more

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.

arXiv:1508.07477•Physical Review B•Dec 8, 2015•34 citations
We consider the position-space information and linear entropies as proxy measures to the average single-site entanglement–quantified using the von Neumann entropy–of the one-dimensional Hubbard model and of a one-dimensional nanostructure system comprised of an array of quantum-dots. Spatial entanglement in the quantum-dot system is also investigated via the three entropies. We appraise the use of the possible proxy measures in the Hubbard model as an approximation to their use for the nanostructure system.
We investigate the Hubbard model, and the extended Hubbard model with and without correlated hopping, as an approximation to the average single-site (or local) entanglement of two-electron one-dimensional quantum dot chains with long range interactions. We focus on the effect of the chain length on the approximation accuracy. We also consider the particle-particle spatial entanglement of the three Hubbard models using the technique of Ref. [3] and compare the accuracy of this approximation to the numerically exact results of the nanostructure system.
We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in MMM wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement.
We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.
The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work, we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the intersite distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the 2d2d2d Hubbard model.
Entanglement has been widely investigated in condensed-matter systems since they are considered good candidates for developing quantum technologies. Additionally, entanglement is a powerful tool to explore quantum phase transitions in strongly correlated systems, with the von Neumann entropy being considered a proper measure of quantum entanglement for pure bipartite systems. For lattice systems, in particular, the single-site entanglement quantifies how much information about the quantum state of the remaining sites can be obtained by a measurement at a single site. Here, we use quantum Monte Carlo calculations to obtain the average single-site entanglement for the two-dimensional Hubbard model in different geometries, probing the effects of varying temperature and interaction strength. We find that the average single-site entanglement signals the quantum phase transitions in such systems, allowing us to identify and characterize signatures of quantum phase transitions even at finite temperatures. We also analyze the relation between entanglement and magnetic susceptibility: in all the geometries considered, we find regimes in which the quantities are roughly linearly connected, revealing their link to the Mott transition.
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 UUU and system size. In both the one- and two-dimensional cases, we find that the subsystem entropy scales proportionally to U2{U}^{2}U2 for weak UUU 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.