A proof of part of Haldane's conjecture on spin chains |
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Authors: | Ian Affleck Elliott H Lieb |
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Institution: | (1) Department of Mathematics, Princeton University, P.O. Box 708, 08544 Princeton, NJ, USA;(2) Department of Physics, Princeton University, P.O. Box 708, 08544 Princeton, NJ, USA |
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Abstract: | It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.Work partially supported by U.S. National Science Foundation grant PHY80-19754 and by the A.P. Sloan Foundation.Work partially supported by U.S. National Science Foundation grant PHY-85-15288. |
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