Post-matrix product state methods: To tangent space and beyond
By J. Haegeman, Tobias J. Osborne, Frank Verstraete. 2013
183 citations recorded by the source corpus.
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/2fbbb41681d22f112740f2ccdc5104843c362ecd
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In Atomic and Molecular Physics, and Optics
- Frank Verstraete
- L. Vanderstraeten
- J. Haegeman
- Reinhold Schneider
- V. Murg
- Gergely Barcza
- Szilárd Szalay
- Max Pfeffer
In Condensed Matter Physics
- Frank Verstraete
- L. Vanderstraeten
- J. Haegeman
- Reinhold Schneider
- V. Murg
- E. Stoudenmire
- Frank Pollmann
- Ivan H. Deutsch
In Numerical Analysis
Citations in the corpus
- Tensor product methods and entanglement optimization for ab initio quantum chemistry (2014, background): “(88) This representation has been developed independently by different authors(76,183,243).”
- Time-evolution methods for matrix-product states (2019, unknown): “Future developments While one should of course not lose sight of new alternative methods to evaluate excitation spectra[87–91] or Green’s functions[92], the direct evaluation of real-time observables will always find interesting applications.”
- Tangent-space methods for uniform matrix product states (2018, methodology): “Therefore, it makes sense to associate a tangent space [15] to every point |Ψ(A)〉.”