Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain

Alba, Vincenzo; Saha, Kush; Haque, Masudul

doi:10.1088/1742-5468/2013/10/p10018

Cited by 16 publications

(18 citation statements)

References 35 publications

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“…It is unclear whether such substructures might survive when the degenerate states are taken into account, or when higher-order corrections are included. In addition, substructures in the XXZ spectrum are often heavily determined by boundary conditions [110,112,120]. So, they can be expected to be different for periodic and open boundary conditions.…”

Section: A First Order Perturbation Expansionmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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Section: A First Order Perturbation Expansionmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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“…Unusual behavior in highly excited states is a hallmark of many-body localization [5], and a related phenomenon is described in [6][7][8]. Similar behavior also occurs in the integrable XXZ chain, at least in excited states with zero energy density [9,10].…”

Section: Introductionmentioning

confidence: 99%

Long coherence times for edge spins

Kemp¹,

Yao²,

Laumann³

et al. 2017

J. Stat. Mech.

158

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We show that in certain one-dimensional spin chains with open boundary conditions, the edge spins retain memory of their initial state for very long times. The long coherence times do not require disorder, only an ordered phase. In the integrable Ising and XYZ chains, the presence of a strong zero mode means the coherence time is infinite, even at infinite temperature. When Ising is perturbed by interactions breaking the integrability, the coherence time remains exponentially long in the perturbing couplings. We show that this is a consequence of an edge "almost" strong zero mode that almost commutes with the Hamiltonian. We compute this operator explicitly, allowing us to estimate accurately the plateau value of edge spin autocorrelator. arXiv:1701.00797v2 [cond-mat.stat-mech]

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“…It infers that the quantum correlation between the 1st neighbor spins is maximal at the critical point ∆ = 1 [41]. The critical point ∆ = −1 is not conformal and it has recently attracted some attention [42][43][44]. It is shown that the finite-size corrections to the energy per site non trivially vanish in the ferromagnetic ∆ → −1 + isotropic limit.…”

Section: Introductionmentioning

confidence: 99%

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Mahdavifar¹,

Jafari²

2017

Phys. Rev. A

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One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.

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Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain

Cited by 16 publications

References 35 publications

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Long coherence times for edge spins

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

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