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<p>We compute the spectrum of the finite open <i>XX</i> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月9日

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  • Jan Felipe van Diejen,
  • Andrés Soledispa Tibán,
  • Adrián Vidal

摘要

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.