The Spectrum of the Finite Open XX Quantum Spin Chain with Transverse Magnetic Boundary Fields via Orthogonal Polynomials

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

Annales Henri Poincaré Pub Date : 2025-04-09 DOI:10.1007/s00023-025-01564-0

Jan Felipe van Diejen, Andrés Soledispa Tibán, Adrián Vidal

引用次数: 0

Abstract

We compute the spectrum of the finite open XX quantum spin chain with transverse magnetic boundary fields in terms of the roots of a two-parameter orthogonal family of Bernstein–Szegö polynomials. Estimates are presented for the locations of these roots. This enables the construction of an explicit eigenbasis diagonalizing the spin chain in terms of Slater determinants built from a one-parameter subfamily of the Bernstein–Szegö polynomials evaluated on the spectrum.

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用正交多项式研究具有横向磁场边界场的有限开放XX量子自旋链的谱

我们用两参数正交族Bernstein-Szegö多项式的根计算了具有横向磁场边界场的有限开放XX量子自旋链的谱。对这些根的位置提出了估计。这使得一个显式的特征基的构造对角化自旋链的斯莱特行列式，从一个单参数亚族的Bernstein-Szegö多项式在谱上评估。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.