Geometry of variational methods: dynamics of closed quantum systems

@article{Hackl2020GeometryOV,
  title={Geometry of variational methods: dynamics of closed quantum systems},
  author={L. Hackl and Tommaso Guaita and T. Shi and J. Haegeman and E. Demler and I. Cirac},
  journal={arXiv: Quantum Physics},
  year={2020}
}
We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kahler and non-Kahler. Traditional variational methods typically require the variational family to be a Kahler manifold, where multiplication… Expand

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References

SHOWING 1-10 OF 140 REFERENCES
Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
Quantum fields in curved space-times
  • A. Ashtekar, A. Magnon
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1975
Coherent states: Theory and some Applications
Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach.
Local-in-Time Error in Variational Quantum Dynamics.
Post-matrix product state methods: To tangent space and beyond
Geometry of Matrix Product States: metric, parallel transport and curvature
...
1
2
3
4
5
...