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Chinese Physics B

Revealing EPR Steering and Bell Nonlocality via Local Filtering Operation in Fermi-Hubbard Model on Graphene Honeycomb Lattice

Hao Wang

Published Mar 12, 2026• 0 citations
Publisher

Abstract

Abstract In this paper, we study the dynamics of Bell nonlocality and quantum steering of Fermi-Hubbard model on graphene honeycomb lattice. In the model, Bell nonlocality and Einstein-Podolski-Rosen steering have been exactly solved with and without the local flltering operation (LFO). The influence of flnite temperature, on-site Coulomb repulsion, and nearest-neighbor repulsion on Bell nonlocality and quantum steerability is investigated. The equilibrium state established through the competition between nearest-neighbor and on-site Coulomb repulsions efiectively balances nonlocal quantum correlations. The interplay of these competing interactions drives the system toward a separable regime, wherein both Bell nonlocality and quantum steering violations are completely suppressed. Furthermore, the flltering process not only enhances the degree of quantum steering and Bell nonlocality but also contracts their operational range. These results will provide more theoretical guidance and greater practical signiflcance for the manipulation of Bell nonlocality and quantum steering within graphene systems.

DOI
10.1088/1674-1056/ae50e0

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Abstract In this paper, we study the dynamics of Bell nonlocality and quantum steering of Fermi-Hubbard model on graphene honeycomb lattice. In the model, Bell nonlocality and Einstein-Podolski-Rosen steering have been exactly solved with and without the local flltering operation (LFO). The influence of flnite temperature, on-site Coulomb repulsion, and nearest-neighbor repulsion on Bell nonlocality and quantum steerability is investigated. The equilibrium state established through the competition between nearest-neighbor and on-site Coulomb repulsions efiectively balances nonlocal quantum correlations. The interplay of these competing interactions drives the system toward a separable regime, wherein both Bell nonlocality and quantum steering violations are completely suppressed. Furthermore, the flltering process not only enhances the degree of quantum steering and Bell nonlocality but also contracts their operational range. These results will provide more theoretical guidance and greater practical signiflcance for the manipulation of Bell nonlocality and quantum steering within graphene systems.
We study the dynamics of quantum nonlocality in a graphene-inspired two-carbon-atom Fermi-Hubbard system. Three measures of quantum correlation are examined. These are the entanglement of formation, the Einstein-Podolsky-Rosen steering, and the violation of the CHSH inequality. The system is modelled by the extended Hubbard Hamiltonian with on-site and nearest-neighbour Coulomb interactions, and intrinsic decoherence is described by Milburn's model. The half-filled sector, the two-qubit encoding and the initial state are specified. The two Coulomb energies act through their difference alone. This difference fixes a fast timescale set by the charge gap and a slow timescale set by the superexchange splitting. The level of correlation that the system reaches is fixed by the preparation. Intrinsic decoherence removes the fast component before the slow one, so the lifetime of the nonlocal correlations grows as the difference of the Coulomb energies grows. The entanglement of formation survives after the nonlocal measures have vanished.
Abstract In this work, we mainly study Bell nonlocality and quantum steerability of two-coupled double quantum dots (DQDs) system via local filtering operation. We compare and analyze the influence of the Coulomb potential, temperature, tunneling parameter and local filtering operation on quantum steering and Bell nonlocality in the system. The results show that quantum steering and nonlocality first increase and then decrease but never vanish even for the stronger value of the Coulomb potential. Quantum steering and Bell nonlocality would degrade with the increase of temperature. The filtering process does not increase the degree of steerability, but decreases the range of quantum steerability. In addition, it is noteworthy that a peculiar phenomenon exists: the Einstein–Podolsky–Rosen (EPR) steering asymmetry between Alice and Bob first increase, then decrease to zero and finally increases as the tunneling strength increases. However, this phenomenon does not appear with no operation between Alice and Bob.
Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.
We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional renormalization group scheme, which allows for highly resolved calculations of wave-vector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure nth{n}^{\text{th}}nth nearest-neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when nonlocal density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough nonlocal terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semimetallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second-nearest-neighbor interactions is not realized in our results with high momentum resolution.
The Hubbard and extended Hubbard models on the honeycomb lattice can be seen as prototype models of a single-layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the absence of a sign problem at half-filling, we study this problem with clusters up to 96 sites with the determinant quantum Monte Carlo method as an impurity solver for the dynamical cluster approximation at finite temperatures. After determining the stability of the semimetallic phase to interaction-induced spin-density wave (SDW), charge-density wave (CDW), and Mott insulating phases, we study the single-particle dynamics of the Dirac fermions. We show that when spontaneous symmetry breaking is avoided, the semimetallic phase is a stable Fermi liquid in the presence of repulsive interactions and that Kondo screening dominates the low temperature regime, even though there is a $\ensuremath{\rho}(\ensuremath{\omega})=|\ensuremath{\omega}|$ type local density of states. We also investigate the impact of the correlation effects on the renormalization of the Fermi velocity vF{v}_{F}vF​. We find that vF{v}_{F}vF​ is not renormalized when only on-site repulsion UUU is present, but that near-neighbor repulsion VVV does renormalize vF{v}_{F}vF​. This may explain the variations between different measurements of vF{v}_{F}vF​ in graphene.
By using the Born Markovian master equation, we study the relationship among the Einstein-Podolsky-Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.