Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models

Moyuru Kurita, Youhei Yamaji, Satoshi Morita, Masatoshi Imada

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU(2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin-orbit interaction coexist.

Original languageEnglish
Article number035122
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume92
Issue number3
DOIs
Publication statusPublished - 2015 Jul 10
Externally publishedYes

Fingerprint

Wave functions
spin-orbit interactions
Monte Carlo method
Orbits
Monte Carlo methods
wave functions
quantum numbers
Ground state
projection
Hubbard model
ground state
Hamiltonians
Electron correlations
complex numbers
Liquids
symmetry
liquids
Conservation
Momentum
Demonstrations

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models. / Kurita, Moyuru; Yamaji, Youhei; Morita, Satoshi; Imada, Masatoshi.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 92, No. 3, 035122, 10.07.2015.

Research output: Contribution to journalArticle

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