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issp-center-dev / mVMC

A numerical solver package for a wide range of quantum lattice models based on many-variable Variational Monte Carlo method
http://www.pasums.issp.u-tokyo.ac.jp/mvmc/en/
GNU General Public License v3.0
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Hubbard model with complex hopping term #54

Closed sinnnnnnn closed 5 months ago

sinnnnnnn commented 5 months ago

Dear mVMC Developers,

I recently came across the application of mVMC in studying the WSe2 TMD (Transition Metal Dichalcogenides) system, specifically modeled as the Moire Hubbard model on a triangular lattice. I want to replicate some of these findings. A notable difference of this model is that the hopping term (t=e^iΦσ) is a complex number, where the sign of t's imaginary part varies with the spin σ. Initially, to ensure the accuracy of my results, I employed the Exact Diagonalization (ED) method on a 1D Hubbard chain.

First, I used the mVMC standard mode to compute the conventional Hubbard model (where t remains unchanged with spin) and set L=4, t=1.0,0.5, and U=10. It works well, the ground state energy from mVMC is consistent with that from ED.

Next, I modify the input file (trans.def) to implement the Moire Hubbard model. Actually, the following changes were made：

Before： 1 0 0 0 1.000000000000000 0.50000000000000 0 0 1 0 1.000000000000000 -0.50000000000000 0 1 1 1 1.000000000000000 0.50000000000000 1 1 0 1 1.000000000000000 -0.50000000000000 After： 1 0 0 0 1.000000000000000 0.50000000000000 0 0 1 0 1.000000000000000 -0.50000000000000 0 1 1 1 1.000000000000000 -0.50000000000000 1 1 0 1 1.000000000000000 0.50000000000000 However, the energy differs significantly from ED. I look forward to any insights or suggestions you may have regarding this matter. Best regards

k-ido commented 5 months ago

If the parameter set for which you did not get accurate results is "Before" one, your target system has spin-dependent transfers. For this case, I recommend that you use "OrbitalGeneral", or both "Orbital" and "OrbitalParallel". https://issp-center-dev.github.io/mVMC/doc/master/en/expert.html#orbitalparallel-file https://issp-center-dev.github.io/mVMC/doc/master/en/expert.html#orbitalgeneral-file

"OrbitalGeneral" and "OrbitalParallel" can be generated by specifying "HubbardGC" in standard mode. https://issp-center-dev.github.io/mVMC/doc/master/en/standard.html

sinnnnnnn commented 5 months ago

Dear Ido， Thanks for your advice! I know how to prepare input files now.

Best Regards