2014 Fiscal Year Annual Research Report
| Project/Area Number |
13F03802
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| Research Institution | The University of Tokyo |
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Principal Investigator |
押川 正毅 東京大学, 物性研究所, 教授 (50262043)
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| Co-Investigator(Kenkyū-buntansha) |
LAJKO Miklos 東京大学, 物性研究所, 外国人特別研究員
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | SU(N) Heisenberg model / Gutzwilller projection / chiral spin liquid / Kondo interaction / anomalous Hall-effect |
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| Outline of Annual Research Achievements |
SU(N) symmetric Heisenberg models
We used Gutzwiller projection approach to study the SU(6) symmetric Heisenberg model on the honeycomb lattice. In agreement with exact diagonalization results, variational Monte Carlo calculations on the Gutzwiller projected states suggest that in contrast to previous mean-field results, a plaquette ordered phase is energetically preferred over a chiral spin liquid phase at the nearest neighbor Heisenberg point. introducing a weak ring exchange interaction around the hexagonal plaquettes leads to a phase transition to the chiral liquid phase.
By improving the Monte Carlo algorithm we calculated the matrix elements of the Hamiltonian and the overlaps between different Gutzwiller projected states, allowing to further optimize the variational approximation of the ground state and low energy excitations. We also studied the SU(5) triangular lattice. In the nearest neighbor Heisenberg point exact diagonalization shows an alternating nonzero chirality on the triangular plaquettes, which gives place to a uniform chiral spin liquid upon coupling the chirality to a uniform external field.
Study of Kondo lattice models
The aim of the project is to address the experimental findings of the group of Satoru Nakatsuji of anomalous Hall-effect in fcc f-electron systems. We carried out preliminary classical Monte Carlo calculations which suggests that a Kondo-interaction itself can lead to nonzero spin scalar chirality of the localized spins, resulting in nonzero Hall-conductance without magnetic field.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
My work on the SU(N) Heisenberg models provided interesting and unforeseen insights into the low energy physics and also the topological aspects of the ground state of the SU(N) spin systems. Manuscripts are under preparation for both the SU(6) honeycomb and SU(5) triangular case (planned submission: 2015 May/June).
The work on the fcc Kondo-lattice model is behind the planned schedule, due to longer than expected algorithm implementation and testing, and increased work time on the Gutzwiller projection study.
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| Strategy for Future Research Activity |
Studying the topological aspects of SU(N) chiral spin liquids
Using Gutzwiller projection I found N low lying states in the chiral liquid phases, which correspond to the N-fold degenerate ground state on a torus. Using Monte Carlo algorithm we can calculate the elements of the modular matrices, which provide information on the self- and pair statistics of the anyonic quasiparticles thus characterizing the topological order, and might allow us to identify the underlying field theory.
Study of Kondo lattice models
The Langevin equation based approach will allow to make calculations effectively for finite temperatures and larger system sizes, allowing us to study the conductance and the Hall-conductance as a function of the temperature, which would provide comparison for experimental results.
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Research Products
(2 results)
