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Hidden local gauge invariance in integrable magnetic chains
Institution:1. Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA 94720, USA;2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;3. Department of Physics, Washington University in St. Louis, St. Louis, MO 63130, USA;4. Institute of Materials Science and Engineering, Washington University in St. Louis, St. Louis, MO 63130, USA;5. National Engineering Center of Electromagnetic Radiation Control Materials, University of Electronic Science and Technology of China, Chengdu, Jiangsu 610054, RP China;6. The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;1. Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA;2. Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455, USA;3. Chemical Physics Theory Group, Department of Chemistry and Department of Computer Science, University of Toronto, Toronto, ON M5S 3H6, Canada;4. Vector Institute for Artificial Intelligence, Toronto, ON M5S 1M1, Canada;5. Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR) Senior Fellow, Toronto, ON M5S 1M1, Canada;6. Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, 5735 South Ellis Avenue, Chicago, IL 60637, USA
Abstract:It is shown that local gauge transformations preserve the integrability of one-dimensional quantum Heisenberg chains. Abelian U(1) gauge transformations associated to z-rotations appear in the XXZ model which is worked out in detail. The exact energy spectrum derived by the Bethe ansatz turns out to be gauge-invariant whereas the eigenvectors are explicitly gauge-dependent. Isotropic XXX chains exhibit SU(2) ⊗ Z2 gauge invariance properties and anisotropic XYZ chains possess discrete Z2 ⊗ Z2 gauge invariance.
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