KMS states on Quantum Grammars

Details KMS states on Quantum Grammars KMS states on Quantum Grammars

1999-06-09

arxiv.org/abs/math-ph/9906009v1

Journal of Mathematical Physics, 2000, No. 7, pp. 4508-4520

Physics

Mathematical Physics

22 pages

Scientific paper

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results. We prove existence of the dynamics in both Schroedinger and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We show (for high temperatures) that for each system where the lattice undergoes quantum evolution, there is a natural scaling leading to a quantum spin system on a fixed lattice, defined by a renormalized Hamiltonian.

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