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2020

Locality estimes for complex time evolution in 1D

Pérez-García, David, Pérez-Hernández, Antonio

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It is a generalized belief that there are no thermal phase transitions in short range 1D quantum systems.

However, the only known case for which this is rigorously proven is for the particular case of finite range translational invariant interactions.
The proof was obtained by Araki in his seminal paper of 1969 as a consequence of pioneering locality estimates for the time-evolution operator that allowed him to prove its analiticity on the whole complex plane, when applied to a local observable.
However, as for now there is no mathematical proof of the abscence of 1D thermal phase transitions if one allows exponential tails in the interactions.

Locality estimes for complex time evolution in 1D · Around

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D. W. Robinson
1968
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D. Ruelle
1968
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H. Araki
1969
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F. Dyson
1969
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D. Ruelle
1969
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C. Domb and M.S. Green
1972
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E. Lieb and D. Robinson
1972
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H. Araki
1973
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R. L. Dobrushin
1973
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H. Araki
1975
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A. Kishimoto
1976
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O. Bratteli and D. Robinson
1987
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O. Bratteli and D. Robinson
1997
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V. Golodets and S. V Neshveyev
1998
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