Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems
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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.
KeywordsGround state quantum lattice system
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