Embedding generalized thimble HMC into worldvolume HMC improves ergodicity and phase-space exploration for sign-problem mitigation in 2D doped Hubbard model simulations, enabling larger lattices and controlled extrapolations.
Tempered transitions between thimbles
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abstract
Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0+1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.
fields
cond-mat.str-el 2years
2025 2representative citing papers
WV-HMC computes number and energy densities for the doped 2D Hubbard model on 6x6 and 8x8 lattices at U/t=8 and T/t≈0.156, showing effectiveness where standard DQMC fails.
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Enhancing the ergodicity of Worldvolume HMC via embedding generalized thimble HMC
Embedding generalized thimble HMC into worldvolume HMC improves ergodicity and phase-space exploration for sign-problem mitigation in 2D doped Hubbard model simulations, enabling larger lattices and controlled extrapolations.
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Applying the Worldvolume Hybrid Monte Carlo method to the Hubbard model away from half filling
WV-HMC computes number and energy densities for the doped 2D Hubbard model on 6x6 and 8x8 lattices at U/t=8 and T/t≈0.156, showing effectiveness where standard DQMC fails.