A convenient frontend for calculating dynamical correlation functions and related observables based on matrix-product states time evolution methods.
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The symbolic operator representation of a quantum lattice system in condensed matter physics is based on the package
QuantumLattices
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The matrix-product states time evolution methods such as TEBD, MPO
$W^{II}$ and TDVP are based on packagesITensors
andMPSKit
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The bechmark of dynamical correlation functions and related observables is the result from exact diagonalization method based on the packages
ExactDiagonalization
Please type ]
in the REPL to use the package mode, then type this command:
pkg>add DCorrelators
Currently unavailable
If the
where
Dividing
If the times
where
To make it a per unit frequency interval, one need to divide by the spacing of the discrete frequency mode and the Fourier amlitudes are given by,
Although a Fourier series is designed to represent functions that are periodic, one can assume that the finite data sequence can be periodically repeated, which leads to the time at index
By use of double Fourier transforms, one can obtain the
With
the continuous form is as follows
The real-space and real-time correlation function
Finally, one gets,
Here, the matrix-product states time evolution methods are implemented to solve the state
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Wysin G M. Magnetic Excitations and Geometric Confinement[M]. Philadelphia, USA: IOP, 2015.
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Paeckel S, Köhler T, Swoboda A, et al. Time-evolution methods for matrix-product states[J]. Annals of Physics, 2019, 411: 167998.
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Due to the fast development of this package, releases with different minor version numbers are not guaranteed to be compatible with previous ones before the release of v1.0.0. Comments are welcomed in the issues.