Analytic properties of Gibbs states for a class of one-dimensional lattice quantum systems

1993 ◽  
Vol 94 (1) ◽  
pp. 71-88
Author(s):  
N. U. Khudoinazarov
Keyword(s):  
Quantum Systems ◽  
Gibbs States ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Lattice Quantum

scholarly journals Asymmetric butterfly velocities in 2-local Hamiltonians

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Yong-Liang Zhang ◽  
Vedika Khemani
Keyword(s):  
Correlation Functions ◽  
Quantum Systems ◽  
Information Propagation ◽  
Local Interactions ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Local Operators ◽  
Left And Right ◽  
Model Hamiltonians

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a ``butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

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