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Conformal Invariance and the Spectrum of the XXZ Chain

Francisco Castilho Alcaraz, Michael N. Barber, Murray T. Batchelor

Published Jan 1, 1988• 1 citation
Publisher
DOI
10.1016/b978-0-444-87109-1.50036-4

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Numerical solutions of the Bethe-Ansatz equations for the eigenenergies of XXZ Hamiltonian on very large chains are used to identify, via conformal invariance, the scaling dimensions of various two-dimensional models. With periodic boundary conditions, eight-vertex and Gaussian model operators are found. The scaling dimensions of the Ashkin-Teller and Potts models are obtained by the exact relating of eigenstates of their quantum Hamiltonians to those of the XXZ chain with modified boundary conditions. The irrelevant operators governing the dominant finite-size corrections are also identified.

Physical Review Letters•Feb 23, 1987•170 citations
Numerical solutions of the Bethe-Ansatz equations for the eigenenergies of XXZ Hamiltonian on very large chains are used to identify, via conformal invariance, the scaling dimensions of various two-dimensional models. With periodic boundary conditions, eight-vertex and Gaussian model operators are found. The scaling dimensions of the Ashkin-Teller and Potts models are obtained by the exact relating of eigenstates of their quantum Hamiltonians to those of the XXZ chain with modified boundary conditions. The irrelevant operators governing the dominant finite-size corrections are also identified.