Floating block method for quantum Monte Carlo simulations

Abstract

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ${}^4$He, ${}^8$Be, ${}^{12}$C, and ${}^{16}$O nuclei over a range of local and non-local interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

6 pages, 7 figures + 4 pages, 1 figure (supplemental materials). Figures showing the quantum phase transition between a Bose gas of alpha particles and nuclear liquid have been improved

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• Monte Carlo study of two-dimensional Bose-Hubbard model
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• Applications of quantum Monte Carlo methods in condensed systems
• Lattice field theory simulations of graphene
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Cited by in corpus (5)

• Eigenvector Continuation and Projection-Based Emulators
• Lattice Effective Field Theory Simulations of Nuclei
• Emulators for scarce and noisy data: application to auxiliary field diffusion Monte Carlo for the deuteron
• Quantum techniques for eigenvalue problems
• Searching for the Tetraneutron Resonance on the Lattice