The spin-1/2 XXZ Heisenberg chain, the quantum algebra U[sub q][sl(2)], and duality transformations for minimal models

Journal Article · Tue Jun 01 00:00:00 EDT 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01049955· OSTI ID:5918825

Grimm, U ^[1]; Schuetz, G ^[2]

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1. Univ. of Melbourne, Parkville, Victoria (Australia)
2. Weizmann Institute, Rohovot (Israel)

The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c < 1, including the unitary and nonunitary minimal series. Taking into account the half-integer angular momentum sectors-which correspond to chains with an odd number of sites-in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to new types of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which, however, differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite XXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involving U[sub q][sl(2)] quantum algebra transformations. 35 refs., 3 tabs.

• OSTI ID: 5918825
• Journal Information: Journal of Statistical Physics; (United States), Vol. 71:5-6; ISSN 0022-4715
• Country of Publication: United States
• Language: English

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