Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory |
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| Affiliation: | 1. Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA;2. Canadian Institute for Advanced Research and Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada;3. Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan;4. S.Ph.T., C.E.N. Saclay, 91191 Gif-sur-Yvette, Cedex, France;1. Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan;2. Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada;3. Irving K. Barber School of Arts and Sciences, University of British Columbia – Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7, Canada;1. Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, PR China;2. College of Science, Nanjing Tech University, Nanjing 211816, PR China;3. Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, PR China;1. School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran;2. Laboratoire de Mathématiques et Physique Théorique CNRS-UMR 7350, Fédération Denis Poisson, Université François-Rabelais Tours, Parc de Grandmont, 37200 Tours, France |
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| Abstract: | We study a single particle diffusing on a triangular lattice and interacting with a heat bath, using boundary conformal field theory (CFT) and exact integrability techniques. We derive a correspondence between the phase diagram of this problem and that recently obtained for the 2-dimensional 3-state Potts model with a boundary. Exact results are obtained on phases with intermediate mobilities. These correspond to nontrivial boundary states in a conformal field theory with 2 free bosons which we explicitly construct for the first time. These conformally invariant boundary conditions are not simply products of Dirichlet and Neumann ones and unlike those trivial boundary conditions, are not invariant under a Heisenberg algebra. |
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