Path-integral Mayer-sampling calculations of the quantum Boltzmann contribution to virial coefficients of helium-4

We present Mayer-sampling Monte Carlo calculations of the quantum Boltzmann contribution to the virial coefficients B_n, as defined by path integrals, for n 2 to 4 and for temperatures from 2.6 K to 1000 K, using state-of-the-art ab initio potentials for interactions within pairs and triplets of helium-4 atoms. Effects of exchange are not included. The vapor-liquid critical temperature of the resulting fourth-order virial equation of state is 5.033(16) K, a value only 3 less than the critical temperature of helium-4: 5.19 K. We describe an approach for parsing the Boltzmann contribution into components that reduce the number of Mayer-sampling Monte Carlo steps required for components with large per-step time requirements. We estimate that in this manner the calculation of the Boltzmann contribution to B₃ at 2.6 K is completed at least 100 times faster than the previously reported approach.