On the thermodynamics of fermions at any temperature based on parametrized partition function

Abstract

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of Fermi systems with numerical simulation. As an example, we present energies and heat capacities for 10 noninteracting fermions and 10 interacting fermions (more fermions are provided in the appendix) and show good agreement with the analytical result for noninteracting case.

arXiv comment20 pages, 7 figures, Accepted by Physical Review E

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• First principles simulations of dense hydrogen
• From Density Response to Energy Functionals and Back: An ab initio perspective on Matter Under Extreme Conditions
• Normal liquid ${}^3$He studied by Path Integral Monte Carlo with a parametrized partition function
• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
• Accelerated free energy estimation in ab initio path integral Monte Carlo simulations
• GPU acceleration of ab initio simulations of large-scale identical particles based on path integral molecular dynamics
• Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Kinetic contribution to the arbitrary order odd frequency moments of the dynamic structure factor
• Combining Harmonic Sampling with the Worm Algorithm to Improve the Efficiency of Path Integral Monte Carlo