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

Physical Review A

Interplay between charge and spin thermal entanglement in Hubbard dimers

Fabiana Souza, G. M. A. Almeida, M. L. Lyra, Maria S. S. Pereira

Published Sep 29, 2020• 12 citations
Publisher

Abstract

We study quantum entanglement in half-filled Hubbard dimers at finite temperatures under an external magnetic field. Due to the itinerant nature of the electrons and their fundamental indistinguishability, we employ a site-based evaluation of entanglement via the concurrence in three distinct sectors of the Hilbert space, namely the charge, zero-, and single-spin subspaces. At zero temperature these measures can be combined to produce an accurate estimate of the entanglement entropy. For finite temperatures we show that those concurrences display reentrant behavior upon varying the magnetic field. Furthermore, we unveil that charge and spin quantum correlations are quite distinctly degraded by thermal fluctuations.

DOI
10.1103/physreva.102.032421

Related papers

Thermal entanglement witness for interacting itinerant fermion systems

André Neves Ribeiro, Cláudio Andrade Macedo

The Hubbard model describes interacting itinerant fermion systems and is the simplest model capable of describing the essential physics of strongly correlated electron systems. In this model, both spin correlations and charge correlations are important for the entanglement, thus the magnetic susceptibility is not an appropriate thermal entanglement witness. The specific heat reflects spin correlations and charge correlations. We obtain a relation that permits the specific heat to be used directly as a thermal entanglement witness. We calculate, away from half filling, the entanglement critical temperature ${T}_{E}$, below which entanglement is detected, for small linear clusters and the hypercubic lattice in the limit of infinite dimensions by using the exact numerical diagonalization method and the dynamical mean-field theory, respectively. We find, in both cases, that ${T}_{E}$ increases with increasing strength of the on-site Coulomb repulsion $U$.

Physical Review A•Aug 20, 2012•3 citations

Thermal Entanglement in Spin-Dimer V 4+ with a Strong Magnetic Field

Zhang Guo-Feng, Liang Jiu-Qing, Qiwei Yan

We study the entanglement in Heisenberg dimer single molecular magnets V 4+ with a strong magnetic field by means of the measure of entanglement called ``concurrence'' and find that thermal entanglement exists for both the ferromagnetic (FM) and antiferromagnetic (AFM) cases. In the FM case, entanglement vanishes for anisotropic parameter λ = 0 while in the AFM case, entanglement exits in the whole region of anisotropic parameter 0⩽λ⩽1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.

Chinese Physics Letters•Mar 26, 2003•14 citations

Phase diagram and re-entrant fermionic entanglement in a hybrid Ising-Hubbard ladder

H. S. Sousa, Maria S. S. Pereira, I. N. de Oliveira +2 more

The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.

Physical review. E•May 14, 2018•12 citations

THERMAL ENTANGLEMENT IN SPIN-DIMER V4+ WITH A MAGNETIC FIELD

Guofeng Zhang, Jiu‐Qing Liang

By means of the measure of entanglement called "concurrence" we study the entanglement in Heisenberg dimer single molecular magnets V4+ with a strong magnetic field and find that thermal entanglement exits for both ferromagnetic (FM) and antiferromagnetic (AFM) cases. In FM case entanglement vanishes for anisotropic parameter λ = 0 while in AFM case, entanglement exits in the whole region of anisotropic parameter 0 ≤ λ ≤ 1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.

International Journal of Modern Physics B•Apr 20, 2003•0 citations

Quantum steering in magnetic Heisenberg models at finite temperature

Liang Chen, Ye-Qi Zhang

We investigate the behavior of quantum steering for a pair of quantum qubits described by the Heisenberg model with external magnetic field and in equilibrium with a reservoir at temperature T . Generally, the steerable weight, which is used to identify the steerability, is suppressed by thermal fluctuations. When the magnetic field is vanishing, the steerable weight behaves like the quantum entanglement. When the magnetic field is not zero, the steerable weight is dramatically different from the other quantities used to identify the quantum correlations between the two spins, i.e. , the concurrence, quantum discord and coherence. In the strong magnetic field limit, all of the other quantities we studied are vanishing for the Ising model, while steerable weight tends to one. This demonstrates that the strong transverse magnetic field is helpful to preserve the quantum steerability of the Ising model.

Europhysics Letters (EPL)•Dec 1, 2017•11 citations

Intricately entangled spin and charge diffusion and the coherence-incoherence crossover in the high-dimensional Hubbard model

Gopal Prakash, Syed R. Hassan, M. S. Laad +2 more

Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.

Physica Scripta•Mar 27, 2026•0 citations
We study quantum entanglement in half-filled Hubbard dimers at finite temperatures under an external magnetic field. Due to the itinerant nature of the electrons and their fundamental indistinguishability, we employ a site-based evaluation of entanglement via the concurrence in three distinct sectors of the Hilbert space, namely the charge, zero-, and single-spin subspaces. At zero temperature these measures can be combined to produce an accurate estimate of the entanglement entropy. For finite temperatures we show that those concurrences display reentrant behavior upon varying the magnetic field. Furthermore, we unveil that charge and spin quantum correlations are quite distinctly degraded by thermal fluctuations.
The Hubbard model describes interacting itinerant fermion systems and is the simplest model capable of describing the essential physics of strongly correlated electron systems. In this model, both spin correlations and charge correlations are important for the entanglement, thus the magnetic susceptibility is not an appropriate thermal entanglement witness. The specific heat reflects spin correlations and charge correlations. We obtain a relation that permits the specific heat to be used directly as a thermal entanglement witness. We calculate, away from half filling, the entanglement critical temperature TE{T}_{E}TE​, below which entanglement is detected, for small linear clusters and the hypercubic lattice in the limit of infinite dimensions by using the exact numerical diagonalization method and the dynamical mean-field theory, respectively. We find, in both cases, that TE{T}_{E}TE​ increases with increasing strength of the on-site Coulomb repulsion UUU.
We study the entanglement in Heisenberg dimer single molecular magnets V 4+ with a strong magnetic field by means of the measure of entanglement called ``concurrence'' and find that thermal entanglement exists for both the ferromagnetic (FM) and antiferromagnetic (AFM) cases. In the FM case, entanglement vanishes for anisotropic parameter λ = 0 while in the AFM case, entanglement exits in the whole region of anisotropic parameter 0⩽λ⩽1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.
The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.
By means of the measure of entanglement called "concurrence" we study the entanglement in Heisenberg dimer single molecular magnets V4+ with a strong magnetic field and find that thermal entanglement exits for both ferromagnetic (FM) and antiferromagnetic (AFM) cases. In FM case entanglement vanishes for anisotropic parameter λ = 0 while in AFM case, entanglement exits in the whole region of anisotropic parameter 0 ≤ λ ≤ 1. Entanglement variations with anisotropic parameter λ, magnetic field B and temperature T are evaluated. We find a critical magnetic field at which the concurrence changes sharply from zero to maximum entanglement.
We investigate the behavior of quantum steering for a pair of quantum qubits described by the Heisenberg model with external magnetic field and in equilibrium with a reservoir at temperature T . Generally, the steerable weight, which is used to identify the steerability, is suppressed by thermal fluctuations. When the magnetic field is vanishing, the steerable weight behaves like the quantum entanglement. When the magnetic field is not zero, the steerable weight is dramatically different from the other quantities used to identify the quantum correlations between the two spins, i.e. , the concurrence, quantum discord and coherence. In the strong magnetic field limit, all of the other quantities we studied are vanishing for the Ising model, while steerable weight tends to one. This demonstrates that the strong transverse magnetic field is helpful to preserve the quantum steerability of the Ising model.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.