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.
A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
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abstract
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this approach for a simple fermionic model. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm relies only on the integration of the gradient flow in the numerically stable direction, which gives it a distinct advantage over the other proposed algorithms. We demonstrate the stability and efficiency of the algorithm by applying it to an exactly solvable fermionic model and compare our results with the analytical ones. We report a very good agreement for a certain region in the parameter space where the dominant contribution comes from a single thimble, including a region where standard methods suffer from a severe sign problem. However, we find that there are also regions in the parameter space where the contribution from multiple thimbles is important, even in the continuum limit.
representative citing papers
WV-HMC successfully simulates the doped 2D Hubbard model on 8x8 lattices at U/t=8 and T/t≈0.156 with controlled statistical errors.
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.
citing papers explorer
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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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Analyzing the two-dimensional doped Hubbard model with the Worldvolume HMC method
WV-HMC successfully simulates the doped 2D Hubbard model on 8x8 lattices at U/t=8 and T/t≈0.156 with controlled statistical errors.
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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.