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We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian.
https://doi.org/10.1137/0707001
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https://doi.org/10.1103/PhysRevA.85.040303
J. Chen, Z. Ji, Z. Wei, and B. Zeng, “Correlations in excited states of local hamiltonians,” Phys. Rev. A · 2012
Cited alongside, same era.
https://doi.org/10.1103/PhysRevLett.113.260501
B. Swingle and I. H. Kim, “Reconstructing quantum states from local data,” Physical review letters · 2014
Cited alongside, same era.
https://doi.org/10.1103/PhysRevE.92.012128
H. Kim, M. C. Bañuls, J. I. Cirac, M. B. Hastings, and D. A. Huse, “Slowest local operators in quantum spin chains,” Physical Review E · 2015
Cited alongside, same era.
https://doi.org/10.1103/PhysRevB.91.045138
A. Molnar, N. Schuch, F. Verstraete, and J. I. Cirac, “Approximating gibbs states of local hamiltonians efficiently with projected entangled pair states,” Physical review b · 2015
Cited alongside, same era.
https://doi.org/10.1088/1367-2630/17/5/053021
J. Cho, “Correlations in quantum spin systems from the boundary effect,” New Journal of Physics · 2015
Cited alongside, same era.
https://doi.org/10.1088/1367-2630/18/11/113033
V. Zauner, D. Draxler, L. Vanderstraeten, J. Haegeman, and F. Verstraete, “Symmetry breaking and the geometry of reduced density matrices,” New Journal of Physics · 2016
Later among the works it cites.
https://doi.org/10.1103/PhysRevB.94.144208
T. O’Brien, D. A. Abanin, G. Vidal, and Z. Papić, “Explicit construction of local conserved operators in disordered many-body systems,” Physical Review B · 2016
Later among the works it cites.
https://doi.org/10.1103/PhysRevX.8.021026
J. R. Garrison and T. Grover, “Does a single eigenstate encode the full hamiltonian d?,” Physical Review X · 2018
Closest in time.
https://doi.org/10.1103/PhysRevA.43.2046
J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Physical Review A · 2046
Closest in time.
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