XXZ自旋环纠缠熵的下界

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2023-05-02 DOI:10.1007/s00023-023-01318-w

Christoph Fischbacher, Ruth Schulte

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引用次数: 3

摘要

我们研究了在L大小的环上定义的自由XXZ量子自旋模型，并证明了属于真空基态之上第一能带的某些本征态的二分纠缠熵满足对数校正的面积定律。这尤其适用于与基态之上的最低本征能量相对应的本征态。为此，我们开发了一种新的微扰方法，该方法使我们能够根据Ising模型中相应的还原态来控制XXZ模型中还原态的特征值。在此过程中，我们展示了纤维算子的Combes–Thomas估计，该估计也可以应用于更一般的平移不变图上的离散多粒子薛定谔算子。

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Lower Bound to the Entanglement Entropy of the XXZ Spin Ring

We study the free XXZ quantum spin model defined on a ring of size L and show that the bipartite entanglement entropy of certain eigenstates belonging to the first energy band above the vacuum ground state satisfies a logarithmically corrected area law. This applies in particular to eigenstates corresponding to the lowest eigenenergy above the ground state. To this end, we develop a new perturbational approach, which allows us to control the eigenvalues of reduced states in the XXZ model in terms of the corresponding reduced states in the Ising model. Along the way, we show a Combes–Thomas estimate for fiber operators which can also be applied to discrete many-particle Schrödinger operators on more general translation-invariant graphs.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.