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Journal of Physics Condensed Matter

Quantum correlations in chiral graphene nanoribbons

Xiao-Dong Tan, Cornelie Koop, Xiaoping Liao, Litao Sun

Published Sep 7, 2016• 1 citation
Publisher

Abstract

We compute the entanglement and the quantum discord (QD) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T (canonical ensemble). We show that the entanglement only exists in inter-edge coupled spin pairs, and there is no entanglement between any two spins at the same ribbon edge. By contrast, almost all edge spin pairs can hold non-zero QD, which strongly depends on the ribbon width and the Coulomb repulsion among electrons. More intriguingly, the dominant entanglement always occurs in the pair of nearest abreast spins across the ribbon, and even at room temperature this type of entanglement is still very robust, especially for narrow CGNRs with the weak Coulomb repulsion. These remarkable properties make CGNRs very promising for possible applications in spin-quantum devices.

DOI
10.1088/0953-8984/28/43/435601

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We compute the entanglement and the quantum discord (QD) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T (canonical ensemble). We show that the entanglement only exists in inter-edge coupled spin pairs, and there is no entanglement between any two spins at the same ribbon edge. By contrast, almost all edge spin pairs can hold non-zero QD, which strongly depends on the ribbon width and the Coulomb repulsion among electrons. More intriguingly, the dominant entanglement always occurs in the pair of nearest abreast spins across the ribbon, and even at room temperature this type of entanglement is still very robust, especially for narrow CGNRs with the weak Coulomb repulsion. These remarkable properties make CGNRs very promising for possible applications in spin-quantum devices.
Based on the effective spin-ladder model, we compute the negativity and geometric quantum discord (GQD) between two edge spins in zigzag graphene nanoribbons (ZGNRs) thermalized with a reservoir at temperature T (canonical ensemble). The results show that the entanglement only exists in antiferromagnetically coupled spin pairs, and completely vanishes between any two spins at the same ribbon edge. Intriguingly, the dominant entanglement always occurs in the nearest inter-edge coupled spin pairs, which is very robust even at room temperature. By contrast, almost all edge spin pairs can hold non-zero GQD, which strongly depends on the ribbon width. To get further insight into the properties of entanglement, the multiparticle entanglement (ME) shared between three spins is studied. The results show that ME always exists among spins located at different edges, and it is more robust than the corresponding two-spin entanglement in against the temperature. These remarkable properties make ZGNRs very promising for possible applications in quantum information processing.
Abstract We study the dynamics of entanglement between two edge spins in a zigzag graphene nanoribbon (ZGNR) which is thermalized with a reservoir at temperature T . The results show that the entanglement evolution displays oscillating behaviors in the presence of an external magnetic field. Such oscillating behaviors of entanglement strongly depend on the field frequency and relative location between two inter-edge coupled spins. At some critical field frequencies, the entanglement exhibits a periodic structure. When the temperature is low, the oscillating patterns of entanglement are quite regular and symmetrical. When the temperature is high, the patterns of entanglement evolution occur irregular distortions due to the thermal fluctuations. However, the entanglement between two inter-edge coupled spins in ZGNR still exists a nontrivial value even at room temperature.
In this article, we investigate how various parameters such as the nanoribbon length, temperature, external magnetic field, and Coulomb interactions affect fundamental quantum correlations in zigzag graphene nanoribbons. Using an effective Heisenberg model derived from the Hubbard Hamiltonian, we analyze three essential quantifiers: thermal entanglement, correlated quantum coherence, and local quantum uncertainty. Our results reveal that increasing the ribbon length leads to an exponential reduction of the exchange interaction between edge‐localized electronic states, which causes a gradual decrease of thermal entanglement. Both temperature and Coulomb repulsion significantly reduce the concurrence, while quantum coherence and local quantum uncertainty exhibit greater robustness, maintaining nonclassical correlations even at elevated temperatures. Furthermore, the application of an external magnetic field strongly influences these quantum correlations and enhances their sensitivity to thermal and geometric effects. These findings provide a comprehensive understanding of how structural and environmental parameters govern quantum correlations in graphene‐based nanostructures, offering valuable insights for the design of stable platforms for quantum information processing and spintronic applications.
We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux et al., Nature (London) 531, 489 (2016)], and their descriptions require more sophisticated methods since in this regime conventional methods, like mean-field or density-functional theory with local-density approximation, fail to capture the enhanced quantum fluctuations. Using the unbiased density-matrix renormalization-group algorithm, we calculate the charge gaps with high accuracy for different widths and interaction strengths and compare them with mean-field results. It turns out that the gaps are much smaller in the former case due to the proper treatment of quantum fluctuations. Applying the elements of quantum information theory, we also reveal the entanglement structure inside a ribbon and examine the spectrum of subsystem density matrices to understand the origin of entanglement. We examine the possibility of magnetic ordering and the effect of magnetic field. Our findings are relevant for understanding the gap values in different recent experiments and the deviations between them.
We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.