Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states |
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Authors: | Nilanjana Datta Roberto Fernández Jürg Fröhlich |
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Institution: | (1) Paul Scherrer Institut, CH-8048 Zürich, Switzerland;(2) Institut de Physique Théorique, EPFL, Ecublens, CH-1015 Lausanne, Switzerland;(3) Present address: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina;(4) Institut für Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland |
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Abstract: | Starting from classical lattice systems ind2 dimensions with a regular zerotemperature phase diagram, involving a finite number of periodic ground states, we prove that adding a small quantum perturbation and/or increasing the temperature produce only smooth deformations of their phase diagrams. The quantum perturbations can involve bosons or fermions and can be of infinite range but decaying exponentially fast with the size of the bonds. For fermions, the interactions must be given by monomials of even degree in creation and annihilation operators. Our methods can be applied to some anyonic systems as well. Our analysis is based on an extension of Pirogov-Sinai theory to contour expansions ind+1 dimensions obtained by iteration of the Duhamel formula. |
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Keywords: | Phase diagrams quantum lattice systems Pirogov-Sinai theory contour expansions low-temperature expansions |
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