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Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively.
A.E. Ingham, A note on Fourier Transforms
1934
Earlier work this paper cites.
Lieb, E.H., Schultz, T., and Mattis, D.: Two soluble models of an antiferromagnetic chain, Ann. Phys. 16
1961
Earlier work this paper cites.
E.H. Lieb and D.W. Robinson, The finite group velocity of quantum spin systems
1972
Earlier work this paper cites.
M. Reed, B. Simon, Fourier Analysis, Self-Adjointness
1975
Earlier work this paper cites.
T. Kato, Perturbation Theory for Linear Operators
1980
Earlier work this paper cites.
D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
R. B. Laughlin, Phys. Rev. Lett. 50
1983
Earlier work this paper cites.
T. Kennedy, Long range order in the anisotropic quantum ferromagnetic Heisenberg model
1985
Earlier work this paper cites.
C. Albanese, Unitary dressing transformations and exponential decay below threshold for quantum spin systems. I, II
1990
Earlier work this paper cites.
C. Albanese, Unitary dressing transformations and exponential decay below threshold for quantum spin systems. III, IV
1990
Earlier work this paper cites.
T. Matsui, Uniqueness of the translationally invariant ground state in quantum spin systems
1990
Earlier work this paper cites.
M. Fannes, B. Nachtergaele and R. Werner, Finitely Correlated States on Quantum Spin Chains
1992
Earlier work this paper cites.
T. Kennedy, H. Tasaki, Hidden symmetry breaking and the Haldane phase in S = 1 S=1 quantum spin chains
1992
Earlier work this paper cites.
T. Kennedy, H. Tasaki, Hidden Z 2 × Z 2 Z_{2}\times Z_{2} symmetry breaking in Haldane gap antiferromagnets
1992
Earlier work this paper cites.
C. Borgs and R. Kotecký and D. Ueltschi, Low temperature phase diagrams for quantum perturbations of classical spin systems
1996
Earlier work this paper cites.
E. Dagotto and T.M. Rice, Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
1996
Cited alongside, same era.
N. Datta, R. Fernández and J. Fröhlich, Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states
1996
Cited alongside, same era.
N. Datta, R. Fernández, J. Fröhlich and L. Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy
1996
Cited alongside, same era.
B. Nachtergaele, The spectral gap for some quantum spin chains with discrete symmetry breaking , Commun. Math. Phys. 175
1996
Cited alongside, same era.
J. Dziubańsky, E. Hernández, Band-limited wavelets with subexponential decay
1998
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Later among the works it cites.
T.J. Osborne, Simulating adiabatic evolution of gapped spin systems
2007
Later among the works it cites.
R. Baillie, D. Borwein and J.M. Borwein, Surprising Sinc Sums and Integrals
2008
Later among the works it cites.
Locality of dynamics in general harmonic quantum systems
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Later among the works it cites.
2009
Later among the works it cites.
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Cited alongside, same era.
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2000
Cited alongside, same era.
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Cited alongside, same era.
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Later among the works it cites.
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Lieb-Robinson bounds for commutator-bounded operators
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