Fetching the paper…
Reading the bibliography…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians.
1901
Earlier work this paper cites.
A. Moon, Automorphic equivalence preserves the split property , J. Funct. Analysis 277
1903
Earlier work this paper cites.
1906
Earlier work this paper cites.
1910
Earlier work this paper cites.
1911
Earlier work this paper cites.
J. Ginibre, Existence of phase transitions for quantum lattice systems , Comm. Math. Phys. 14
1969
Earlier work this paper cites.
E.H. Lieb and D.W. Robinson, The finite group velocity of quantum spin systems , Commun. Math. Phys. 28
1972
Earlier work this paper cites.
M. Reed and B. Simon, Fourier analysis, self-adjointness. Methods of modern mathematical physics , vol. 2, Academic Press, 1975
1975
Earlier work this paper cites.
M. Reed and B. Simon, Functional analsyis. Methods of modern mathematical physics , revised and enlarged ed., vol. 1, Academic Press, 1980
1980
Earlier work this paper cites.
L. J. Landau, J. F. Perez, and W. F. Wreszinski, Energy gap, clustering, and the Goldstone theorem in statistical mechanics , J. Stat. Phys. 26
1981
Earlier work this paper cites.
I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki, Valence bond ground states in isotropic quantum antiferromagnets , Comm. Math. Phys. 115
1988
Earlier work this paper cites.
S. Knabe, Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets , J. Stat. Phys. 52
1988
Earlier work this paper cites.
C. Albanese, On the spectrum of the Heisenberg Hamiltonian , J. Stat. Phys. 55
1989
Earlier work this paper cites.
T. Matsui, Uniqueness of the translationally invariant ground state in quantum spin systems , Commun. Math. Phys. 126
1990
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely correlated states of quantum spin chains , Commun. Math. Phys. 144
1992
Earlier work this paper cites.
T. Kennedy and H. Tasaki, Hidden symmetry breaking and the Haldane phase in s = 1 s=1 quantum spin chains , Commun. Math. Phys. 147
1992
Earlier work this paper cites.
T. Kato, Perturbation theory for linear operators , Springer-Verlag, 1995
1995
Earlier work this paper cites.
C. Borgs, R. Kotecký, and D. Ueltschi, Low temperature phase diagrams for quantum perturbations of classical spin systems , Commun. Math. Phys. 181
1996
Earlier work this paper cites.
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 , J. Stat. Phys. 84
1996
Earlier work this paper cites.
N. Datta, J. Fröhlich, L. Rey-Bellet, and R. Fernández, Low-temperature phase diagrams of quantum lattice systems. II. convergent perturbation expansions and stability in systems with infinite degeneracy. , Helv. Phys. Acta 69
1996
Earlier work this paper cites.
B. Nachtergaele, The spectral gap for some quantum spin chains with discrete symmetry breaking , Commun. Math. Phys. 175
1996
Earlier work this paper cites.
O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics , 2 ed., vol. 2, Springer Verlag, 1997
1997
Earlier work this paper cites.
T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain , Lett. Math. Phys. 40
1997
Earlier work this paper cites.
T. Matsui, On the spectra of the kink for ferromagnetic XXZ models , Lett. Math. Phys. 42
1997
Earlier work this paper cites.
J. Weidmann, Lineare Operatoren in Hilberträumen. Teil I. Grundlagen , B.G. Teubner (Stuttgart), 2000
2000
Earlier work this paper cites.
T. Koma, B. Nachtergaele, and S. Starr, The spectral gap for the ferromagnetic spin-J XXZ chain , Adv. Theor. Math. Phys. 5
2001
Earlier work this paper cites.
A. Yu. Kitaev, Fault-tolerant quantum computation by anyons , Ann. Phys. 303
2003
Earlier work this paper cites.
W. Spitzer and S. Starr, Improved bounds on the spectral gap above frustration free ground states of quantum spin chains , Lett. Math. Phys. 63
2003
Earlier work this paper cites.
M. B. Hastings, Lieb-Schultz-Mattis in higher dimensions , Phys. Rev. B 69
2004
Earlier work this paper cites.
M. B. Hastings, Locality in quantum and markov dynamics on lattices and networks , Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
M. B. Hastings and X. G. Wen, Quasi-adiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance , Phys. Rev. B 72
2005
Earlier work this paper cites.
M.A. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases , Phys. Rev. B 71
2005
Earlier work this paper cites.
R. Fernandez, J. Fröhlich, and D. Ueltschi, Mott transitions in lattice boson models. , Commun. Math. Phys. 266
2006
Earlier work this paper cites.
M. B. Hastings and T. Koma, Spectral gap and exponential decay of correlations , Commun. Math. Phys. 265
2006
Cited alongside, same era.
A. Kitaev, Anyons in an exactly solved model and beyond , Annals of Physics 321
2006
Cited alongside, same era.
B. Nachtergaele and R. Sims, Lieb-Robinson bounds and the exponential clustering theorem , Commun. Math. Phys. 265
2006
Cited alongside, same era.
D. A. Yarotsky, Ground states in relatively bounded quantum perturbations of classical lattice systems , Commun. Math. Phys. 261
2006
Cited alongside, same era.
R. Alicki, M. Fannes, and M. Horodecki, A statistical mechanics view on Kitaev’s proposal for quantum memories , J. Phys. A 40
2007
Cited alongside, same era.
S. Bögli, Convergence of sequences of linear opeators and their spectra , Integr. Equ. Oper. Theory 88
2017
Later among the works it cites.
P. Naaijkens, Quantum spin systems on infinite lattices , Lecture Notes in Physics, vol. 933, Springer, 2017
2017
Later among the works it cites.
S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, Quantization of conductance in gapped interacting systems , Ann. Henri Poincaré 19
2018
Later among the works it cites.
2018
Later among the works it cites.
A. Moon and B. Nachtergaele, Stability of gapped ground state phases of spins and fermions in one dimension , J. Math. Phys. 59
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
by same author, Periodic table for topological insulators and superconductors , Advances in theoretical physics : Landau Memorial Conference, Chernogolovka, Russia, 22-26 June 2008, AIP conference proceedings, no. 1134, American Institute of Physics, 2009
2009
Cited alongside, same era.
S. Bravyi, M. Hastings, and S. Michalakis, Topological quantum order: stability under local perturbations , J. Math. Phys. 51
2010
Cited alongside, same era.
I. Klich, On the stability of topological phases on a lattice , Ann. Phys. 325
2010
Cited alongside, same era.
by same author, On spectral gap and split property in quantum spin chains , J. Math. Phys. 51
2010
Cited alongside, same era.
S. Bravyi and M. B. Hastings, A short proof of stability of topological order under local perturbations , Commun. Math. Phys. 307
2011
Cited alongside, same era.
X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems , Phys. Rev. B 83
2011
Cited alongside, same era.
N. Schuch, D. Perez-Garcia, and I. Cirac, Classifying quantum phases using matrix product states and peps , Phys. Rev. B 84
2011
Cited alongside, same era.
by same author, Lieb-Robinson bounds, the spectral flow, and stability for lattice fermion systems , Mathematical Results in Quantum Physics (F. Bonetto, D. Borthwick, E. Harrell, and M. Loss, eds.), Contemporary Mathematics, vol. 717, Amer. Math. Soc., 2018, pp. 93–115
2018
Later among the works it cites.
2018
Later among the works it cites.
2019
Later among the works it cites.
W. De Roeck and M. Salmhofer, Persistence of exponential decay and spectral gaps for interacting fermions , Commun. Math. Phys. 365
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
by same author, The stability of free Fermi Hamiltonians , J. Math. Phys. 60
2019
Later among the works it cites.
2019
Later among the works it cites.
M. Lemm and B. Nachtergaele, Gapped PVBS models for all species numbers and dimensions , Rev. Math. Phys. 31
2019
Later among the works it cites.
by same author, Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms , J. Math. Phys. 60
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
2019
Later among the works it cites.
N. Pomata and T.-C. Wei, AKLT models on decorated square lattices are gapped , Phys. Rev. B 100
2019
Later among the works it cites.
J. Wang, X.-G. Wen, and E. Witten, A new s u ( 2 ) su(2) anomaly , J. Math. Phys. 60
2019
Later among the works it cites.
2019
Later among the works it cites.
by same author, A many-body index for quantum charge transport , Commun. Math. Phys. (2020), 1249–1272
2020
Closest in time.
by same author, Rational indices for quantum ground state sectors , arXiv:2001.06458, 2020
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
T. Koma, Stability of the spectral gap for lattice fermions , arXiv:2005.04548, 2020
2020
Closest in time.
2020
Closest in time.
by same author, A ℤ 2 \mathbb{Z}_{2} -index of symmetry protected topological phases with time reversal symmetry for quantum spin chains , Commun. Math. Phys. 374
2020
Closest in time.
2020
Closest in time.
by same author, Physics and mathematics of quantum many-body systems , Springer Nature, 2020
2020
Closest in time.