Spectrum of a duality-twisted Ising quantum chain

2001/11/19 by Uwe Grimm · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum many-body systems #Random Matrices and Applications #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/35/3/101

published as J. Phys. A: Math. Gen. 35 (2002) L25-L30 · LaTeX, 7 pages, using IOP styles

arxiv created 2001/11/19 · openalex publication_date 2002/01/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalized twisted partition function.

Citations

• The quantum Ising chain with a generalized defect
• Two soluble models of an antiferromagnetic chain

Cited by

• Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
• The bubble algebra: structure of a two-colour Temperley–Lieb Algebra
• TFT construction of RCFT correlators II: unoriented world sheets
• Twofold twist defect chains at criticality

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• Quantum critical point of the Ising chain from boundary effects
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• Energy spectrum and quantum phase transition of the coupled single spin and an infinitely coordinated Ising chain
• The quantum Ising chain with a generalized defect