Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems
- 66 Downloads
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
Unable to display preview. Download preview PDF.
- Albanese, AC. 1990Unitary dressing transformations and exponential decay below threshold for quantum spin systems. CommunMath. Phys.134237272Google Scholar
- Bratteli, O., Robinson, DW 1996Operator Algebras and Quantum Statistical MechanicsSpringer VerlagBerlinVol. 1 Vol. 2Google Scholar
- Datta, N., Kennedy, T. 2002Expansions for one quasiparticle states in spin 1/2 systemsJ. Stat. Phys.108373399Google Scholar
- Fannes, M., Werner, RF 1995Boundary conditions for quantum lattice systemsHelv. Phys. Acta.68635657Google Scholar
- Kennedy, T., Tasaki, H. 1992Hidden Z2× Z2 symmetry breaking in Haldane gap antiferromagnetsPhys. Rev. B45304Google Scholar
- Kirkwood, JR., Thomas, LE. 1983Expansions and phase transitions for the ground states of quantum Ising lattice systemsCommun. Math. Phys.88569580Google Scholar
- Matsui, T. 1990A link between quantum and classical Potts modelsJ. Stat. Phys.59781798Google Scholar