Adiabatic Theorem for Quantum Spin Systems
Bachmann, Sven ; De Roeck, Wojciech ; Fraas, Martin
arXiv, 1612.01505 / Harvested from arXiv
Text on arXiv
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g. in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation $\varepsilon$ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this letter, we prove a version of the adiabatic theorem for gapped ground states of quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo linear response formula for a broad class of gapped interacting systems.
Publié le : 2016-12-05
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  Quantum Physics,  82C10 
@article{1612.01505,
     author = {Bachmann, Sven and De Roeck, Wojciech and Fraas, Martin},
     title = {Adiabatic Theorem for Quantum Spin Systems},
     journal = {arXiv},
     volume = {2016},
     number = {0},
     year = {2016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1612.01505}
}

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin. Adiabatic Theorem for Quantum Spin Systems. arXiv, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/1612.01505/