Floating Block Method for Quantum Monte Carlo Simulations

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 ${}^4\mathrm{He}$, ${}^8\mathrm{Be}$, ${}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}$ nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

Figure 1

The norm matrix calculation of $|N_{ij}{|}^2$ with 12 time steps.

Figure 2

Contour plots for the difference between the EC emulated energy and the corresponding multialpha threshold energies for ${}^8\mathrm{Be}$ in panel (a), ${}^{12}\mathrm{C}$ in panel (b), and ${}^{16}\mathrm{O}$ in panel (c). The dashed lines show the experimental values.