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Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems.
1911
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H. Araki, “Gibbs states of the one-dimensional quantum spin chain,” Commun. Math. Phys. 14
1969
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Elliott H. Lieb and Derek W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys. 28
1972
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Daniel S. Rokhsar and Steven A. Kivelson, “Superconductivity and the quantum hard-core dimer gas,” Phys. Rev. Lett. 61
1988
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Eddy Ardonne, Paul Fendley, and Eduardo Fradkin, “Topological order and conformal quantum critical points,” Annals of Physics 310
2004
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M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions,” Phys. Rev. B 69
2004
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M. B. Hastings and Xiao-Gang Wen, “Quasiadiabatic 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.
Tobias J. Osborne, “Efficient approximation of the dynamics of one-dimensional quantum spin systems,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
S. Bravyi, M. B. Hastings, and F. Verstraete, “Lieb-Robinson bounds and the generation of correlations and topological quantum order,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
Jens Eisert and Tobias J. Osborne, “General entanglement scaling laws from time evolution,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
Matthew B Hastings and Tohru Koma, “Spectral gap and exponential decay of correlations,” Communications in mathematical physics 265
2006
Earlier work this paper cites.
Bruno Nachtergaele and Robert Sims, “Lieb-Robinson bounds and the exponential clustering theorem,” Communications in mathematical physics 265
2006
Earlier work this paper cites.
Jaan Oitmaa, Chris Hamer, and Weihong Zheng, Series expansion methods for strongly interacting lattice models (Cambridge University Press, 2006)
2006
Earlier work this paper cites.
Matthew B Hastings, “An area law for one-dimensional quantum systems,” Journal of statistical mechanics: theory and experiment 2007
2007
Earlier work this paper cites.
Tobias J Osborne, “Simulating adiabatic evolution of gapped spin systems,” Physical Review A—Atomic, Molecular, and Optical Physics 75
2007
Earlier work this paper cites.
Bruno Nachtergaele, Hillel Raz, Benjamin Schlein, and Robert Sims, “Lieb-Robinson bounds for harmonic and anharmonic lattice systems,” Communications in Mathematical Physics 286
2008
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Claudio Castelnovo and Claudio Chamon, “Quantum topological phase transition at the microscopic level,” Phys. Rev. B 77
2008
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Sergey Bravyi, Matthew B. Hastings, and Spyridon Michalakis, “Topological quantum order: Stability under local perturbations,” Journal of Mathematical Physics 51
2010
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2010
Cited alongside, same era.
Norbert Schuch, Sarah K. Harrison, Tobias J. Osborne, and Jens Eisert, “Information propagation for interacting-particle systems,” Phys. Rev. A 84
2011
Cited alongside, same era.
Sven Bachmann, Spyridon Michalakis, Bruno Nachtergaele, and Robert Sims, “Automorphic equivalence within gapped phases of quantum lattice systems,” Communications in Mathematical Physics 309
2012
Cited alongside, same era.
J. Jünemann, A. Cadarso, D. Pérez-García, A. Bermudez, and J. J. García-Ripoll, “Lieb-Robinson bounds for spin-boson lattice models and trapped ions,” Phys. Rev. Lett. 111
2013
Cited alongside, same era.
Jeongwan Haah, Matthew B Hastings, Robin Kothari, and Guang Hao Low, “Quantum algorithm for simulating real time evolution of lattice Hamiltonians,” SIAM Journal on Computing 52
2021
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Yifan Hong and Andrew Lucas, “Fast high-fidelity multiqubit state transfer with long-range interactions,” Phys. Rev. A 103
2021
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Chi-Fang Chen and Andrew Lucas, “Operator growth bounds from graph theory,” Communications in Mathematical Physics 385
2021
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Jiarui Zhao, Zheng Yan, Meng Cheng, and Zi Yang Meng, “Higher-form symmetry breaking at ising transitions,” Phys. Rev. Res. 3
2021
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2022
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2013
Cited alongside, same era.
Baoming Tang, Ehsan Khatami, and Marcos Rigol, “A short introduction to numerical linked-cluster expansions,” Computer Physics Communications 184
2013
Cited alongside, same era.
M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert, “Locality of temperature,” Phys. Rev. X 4
2014
Cited alongside, same era.
Matthew B Hastings and Spyridon Michalakis, “Quantization of Hall conductance for interacting electrons on a torus,” Communications in Mathematical Physics 334
2015
Cited alongside, same era.
Zhe-Xuan Gong, Michael Foss-Feig, Fernando G. S. L. Brandão, and Alexey V. Gorshkov, “Entanglement area laws for long-range interacting systems,” Phys. Rev. Lett. 119
2017
Cited alongside, same era.
Adam Nahum, Sagar Vijay, and Jeongwan Haah, “Operator spreading in random unitary circuits,” Phys. Rev. X 8
2018
Cited alongside, same era.
C. W. von Keyserlingk, Tibor Rakovszky, Frank Pollmann, and S. L. Sondhi, “Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws,” Phys. Rev. X 8
2018
Cited alongside, same era.
Chi-Fang Chen and Andrew Lucas, “Finite speed of quantum scrambling with long range interactions,” Phys. Rev. Lett. 123
2019
Cited alongside, same era.
Later among the works it cites.
Tibor Rakovszky, C. W. von Keyserlingk, and Frank Pollmann, “Dissipation-assisted operator evolution method for capturing hydrodynamic transport,” Phys. Rev. B 105
2022
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2023
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Marius Lemm, Carla Rubiliani, Israel Michael Sigal, and Jingxuan Zhang, “Information propagation in long-range quantum many-body systems,” Phys. Rev. A 108
2023
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2023
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Dominik S. Wild and Álvaro M. Alhambra, “Classical simulation of short-time quantum dynamics,” PRX Quantum 4
2023
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Christopher L. Baldwin, Adam Ehrenberg, Andrew Y. Guo, and Alexey V. Gorshkov, “Disordered Lieb-Robinson bounds in one dimension,” PRX Quantum 4
2023
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2023
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2024
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2024
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Tan Van Vu, Tomotaka Kuwahara, and Keiji Saito, “Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach,” Quantum 8
2024
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2024
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2024
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