High order Chin actions in path integral Monte Carlo

Abstract

High order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action, which is accurate to fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourth and sixth order error coefficients are finely tunable. By optimizing two free parameters entering in the new action we show that the time step error dependence achieved is best fitted with a sixth order law. The computational effort per bead is increased but the total number of beads is greatly reduced, and the efficiency improvement with respect to the primitive approximation is approximately a factor of ten. The Chin action is tested in a one-dimensional harmonic oscillator, a H 2 drop, and bulk liquid 4 He. In all cases a sixth-order law is obtained with values of the number of beads that compare well with the pair action approximation in the stringent test of superfluid 4 He.

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

“…[29], but, in addition, combines two well-known concepts: 1) antisymmetric imaginary time propagators, i.e., determinants [36][37][38], and 2) a fourth-order factorization of the density matrix [39][40][41][42]. Furthermore, since this leads to a significantly more complicated configuration space without any fixed paths, one of us has developed an efficient set of Metropolis Monte Carlo [43] updates that utilize the temporary construction of artificial trajectories [26].…”

“…However, since the kinetic and potential contributions to the Hamiltonian,K andV , do not commute, the low-temperature matrix elements ofρ are not known. To overcome this issue, we use the common group propertyρ(β) = P −1 α=0ρ ( ) of the density matrix, with = β/P , and approximate each of the P factors at a P times higher temperature by the fourthorder factorization [40,41] …”

Superfluidity of metastable glassy bulkpara-hydrogen at low temperature

“…However, the primitive action is too simple to study extreme quantum matter and a better choice for the action is fundamental to reduce both the complexity of the calculation and ergodicity issues. To this end, we have used a high-order Chin action 39,40 to obtain an accurate estimation of the relevant physical quantities with reasonable numeric effort even in the low-temperature regime, where the simulation becomes harder due to the large zero-point motion of particles. We have analyzed the dependence of the p-H 2 energy on the parameter ε and determined an optimal value ε = 1/60 K −1 for which the bias coming from the use of a finite ε value is smaller than the characteristic statistical noise.…”

Momentum Distribution of Liquid $$^{4}$$ 4 He Across the Normal–Superfluid Phase Transition

“…3 allows to reduce the systematic error due to the approximation of the thermal density matrix and eventually to recover "exactly" the expectation values, it is fundamental to use a good approximation for the thermal density matrix in order to reduce the numerical complexity of the algorithm and to avoid ergodicity issues in the sampling. To this end, we use a fourth-order time-step (τ ) approximation [11], based on a symplectic expansion of the propagator due to Chin [12].…”