Variational optimization algorithms for uniform matrix product states
By V. Zauner-Stauber, L. Vanderstraeten, M. Fishman, Frank Verstraete, J. Haegeman. 2017
229 citations recorded by the source corpus.
We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/7618585bdf9278acea944bb61b46a8866e953452
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In Atomic and Molecular Physics, and Optics
- M. Fishman
- E. Stoudenmire
- S. White
- Frank Verstraete
- Frank Pollmann
- L. Vanderstraeten
- J. Hauschild
- J. Haegeman
In Condensed Matter Physics
- Frank Pollmann
- L. Vanderstraeten
- Frank Verstraete
- J. Hauschild
- E. Stoudenmire
- J. Haegeman
- M. Fishman
- S. White
Citations in the corpus
- The ITensor Software Library for Tensor Network Calculations (2020, methodology): “t modern innite MPS and MPO algorithms. This will include the latest developments in obtaining dominant and sub-dominant eigenvalues and MPS eigenvectors of innite MPOs (such as the VUMPS algorithm [56]), obtaining canonical forms of innite MPS and MPOs, and applying innite MPOs to innite MPS. This ”
- Tangent-space methods for uniform matrix product states (2018, methodology): “[16] for the generalization to arbitrary long-range hamiltonians.”
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, methodology): “_bond))/psi.L) print("finalbonddimensions:", psi.chi) To close this chapter, we mention the varitional uniform Matrix Product State algorithm (VUMPS) as a new alternative to iDMRG, see Ref. [67] and references therein. In short, the method can preserve a strict uniform structure of the inn”