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.
Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
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abstract
A unique feature of the hybrid quantum Monte Carlo (HQMC) method is the potential to simulate negative sign free lattice fermion models with subcubic scaling in system size. Here we will revisit the algorithm for various models. We will show that for the Hubbard model the HQMC suffers from ergodicity issues and unbounded forces in the effective action. Solutions to these issues can be found in terms of a complexification of the auxiliary fields. This implementation of the HQMC that does not attempt to regularize the fermionic matrix so as to circumvent the aforementioned singularities does not outperform single spin flip determinantal methods with cubic scaling. On the other hand we will argue that there is a set of models for which the HQMC is very efficient. This class is characterized by effective actions free of singularities. Using the Majorana representation, we show that models such as the Su-Schrieffer-Heeger Hamiltonian at half filling and on a bipartite lattice belong to this class. For this specific model sub-cubic scaling is achieved.
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.