Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

Ashouri, Atefeh; Mahdavifar, S.; Misguich, Grégoire; Vahedi, Javad

doi:10.1002/andp.201900515

Cited by 10 publications

(4 citation statements)

References 71 publications

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“…The single-defect X X Z model has motivated studies of transport behavior in single-defect noninteracting models [38] and searches for minimal chaotic models with electronphonon coupling [39], but it was not until the beginning of 2020 that the model saw a significant resurgence of interest. It has since been employed in studies of many-body quantum chaos [40,41], thermalization [42,43], quantum transport [44,45], and entanglement [46]. In the present work, we show that the onset of chaos due to a local onsite perturbation is not unique to the X X Z model.…”

Section: Introductionmentioning

confidence: 48%

Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional X X Z model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

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Section: Introductionmentioning

confidence: 48%

Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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“…In the following sections, we embark on a distinctive exploration using key observables from the realm of quantum information. In particular, we focus on the entropy of concurrence, quantum discord (QD) and entanglement -all of which have proven to be powerful tools for probing complex quantum systems [42][43][44][45][46] . Our overarching goal is multifaceted: we aim to unravel the existence of the previously outlined phases, to pinpoint the exact locations of critical points within the parameter space, and to engage in a thoughtful discourse on the exotic intermediate region.…”

Section: Modelmentioning

confidence: 99%

Quantum correlations in the frustrated XY model on the honeycomb lattice

Satoori,

Mahdavifar,

Vahedi

2023

Sci Rep

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We have investigated the spin-1/2 XY frustrated antiferromagnetic Heisenberg honeycomb model, which features an intermediate region in its ground state phase diagram that is not well understood. The two dominant phases in the diagram are the quantum spin-liquid (QSL) and the antiferromagnetic Ising order. Quantum correlations suggest that the QSL phase is likely to exhibit entanglement. To explore this possibility, we utilized numerical Lanczos and density matrix renormalization group (DMRG) methods to calculate concurrence, quantum discord (QD), and entanglement entropy. The results of our study indicate the existence of quantum entanglement within the intermediate region, implying a greater probability for the dominance of the quantum spin-liquid (QSL) phase over the antiferromagnetic Ising order. This discovery underscores the importance of considering quantum correlations in comprehending the model’s behavior and provides insight into the complex nature of quantum systems.

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“…Although limited to small system sizes, numerical exact diagonalization has been extensively used to study the properties of excited states of random and disordered spin chains [12,[38][39][40][41]. We perform numerical exact diagonalization on Hamiltonian in Eq.…”

Section: Ed Study Of Entanglement Entropy Scalingmentioning

confidence: 99%

Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions

Mohdeb¹,

Vahedi²,

Kettemann³

2022

Preprint

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Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent α. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to N ∼ 18 spins, we find indications of a delocalization transition at αc ≈ 1 in the middle of the energy spectrum. With RSRG-X and ED, we show that for α > α * the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for α < α * EE displays an algebraic growth with the subsystem size l, S l ∼ l β , with 0 < β < 1. We find that α * ≈ 1 coincides with the delocalization transition αc in the middle of the many-body spectrum.An interpretation of these results based on the structure of the RG rules is proposed, which is due to rainbow proliferation for very long-range interactions α 1. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at α * < 1.

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Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

Cited by 10 publications

References 71 publications

Speck of chaos

Speck of chaos

Quantum correlations in the frustrated XY model on the honeycomb lattice

Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions

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