Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems

Abstract

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that in a finite volume the dependence of the ground state on the boundary condition exponentially decays with the distance to the boundary, which implies in particular that the infinite-volume ground state is unique. Also, equivalent forms of boundary conditions for ground states of general finite quantum systems are discussed.

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Correspondence to D. A. Yarotsky.

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On leave from Institute for Information Transmission Problems, Moscow, Russia.

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Yarotsky, D.A. Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems. J Stat Phys 118, 119–144 (2005). https://doi.org/10.1007/s10955-004-8780-x

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Keywords

  • Ground state
  • quantum lattice system