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arXiv:hep-th/0311085 · International Journal of Modern Physics B

THE MODIFIED XXZ HEISENBERG CHAIN: CONFORMAL INVARIANCE, SURFACE EXPONENTS OF c<1 SYSTEMS AND HIDDEN SYMMETRIES OF FINITE CHAINS

Uwe Grimm, V. Rittenberg

Published Apr 1, 1990• 14 citations
arXivHTMLPDF

Abstract

The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the Uq[SU(2)] symmetric case. It is shown that for a certain “tuning” between the anisotropy angle and the boundary terms the spectra present unexpected degeneracies. These degeneracies are related to the structure of the irreducible representations of the Virasoro algebras for c<1.

DOI
10.1142/s0217979290000474

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The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the Uq[SU(2)] symmetric case. It is shown that for a certain “tuning” between the anisotropy angle and the boundary terms the spectra present unexpected degeneracies. These degeneracies are related to the structure of the irreducible representations of the Virasoro algebras for c<1.
The finite XXZ Heisenberg spin chain with twisted boundary conditions is considered. For the case of an even number of sites N , anisotropy parameter -1/2 and twisting angle 2π/3 the Hamiltonian of the system possesses an eigenvalue -3 N /2. The explicit form of the corresponding eigenvector was found for N ⩽12. Conjecturing that this vector is the ground state of the system we made and verified several conjectures related to the norm of the ground state vector, its component with maximal absolute value and some correlation functions, which have combinatorial nature. In particular, we conjecture that the squared norm of the ground state vector coincides with the number of half-turn symmetric alternating sign N × N matrices.
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