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Communications in Mathematical Physics

, Volume 181, Issue 2, pp 409–446 | Cite as

Low temperature phase diagrams for quantum perturbations of classical spin systems

  • C. Borgs
  • R. Kotecký
  • D. Ueltschi
Article

Abstract

We consider a quantum spin system with Hamiltonian
$$H = H^{(0)} + \lambda V,$$
whereH(0) is diagonal in a basis ∣s〉=⊗ x s x 〉 which may be labeled by the configurationss={sx} of a suitable classical spin system on ℤ d ,
$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$
We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.

Keywords

Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • C. Borgs
    • 1
  • R. Kotecký
    • 2
  • D. Ueltschi
    • 3
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Centre de Physique ThéoriqueCNRSMarseilleFrance
  3. 3.Institut de Physique ThéoriqueEPFLausanneSwitzerland

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