Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

Abstract

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.

29 pages, LaTeX, two references added, redundant figures removed

References in corpus (1)

• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

Cited by in corpus (19)

• Hilbert Space Fragmentation and Commutant Algebras
• Hilbert Space Fragmentation in Open Quantum Systems
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Quantum phases of a chain of strongly interacting anyons
• A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra
• Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity
• Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization
• Russian doll spectrum in a non-Abelian string-net ladder
• Quantum spin chains from Onsager algebras and reflection $K$-matrices
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank $r\ge 1$
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Tensor Product Structure Geometry under Unitary Channels
• On correlation functions in models related to the Temperley-Lieb algebra
• Entanglement cost hierarchies in quantum fragmented mixed states
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model