Quantum Spin Systems at Positive Temperature |
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Authors: | Marek Biskup Lincoln Chayes Shannon Starr |
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Institution: | (1) Department of Mathematics, UCLA, Los Angeles, CA, 90095, U.S.A |
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Abstract: | We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. |
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