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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.
In previous work with Scullard, we defined a graph polynomial P_B(q,T) that gives access to the critical temperature T_c of the q-state Potts model on a general two-dimensional lattice L. It depends on a basis B, containing n x m unit cells of L, and
First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with
We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case.
This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving Renyi entropy growth rates and magnetisation relax
In this letter we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in paper cite{S}. As it turned out, for a special value of the asymmetry parameter $Delta=-1/2$ the Hamiltonia