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The Path Integral Monte Carlo Sign Problem Is Not Always NP-Hard: Harmonic Fermions Can Be Solved in Quadratic Time
Aarif Chaudhary, Jonas Valenzuela, Siu A. Chin
In the Path Integral Monte Carlo (PIMC) simulation of fermions in a harmonic trap, with and without pairwise harmonic interactions, the partition functions for any discrete number…
Simple proof that there is no sign problem in Path Integral Monte Carlo simulations of fermions in one dimension
Siu A. Chin
It is widely known that there is no sign problem in Path Integral Monte Carlo (PIMC) simulations of fermions in one dimension. Yet, as far as the author is aware, there is no direc…
A thousand fermions in a 3D harmonic trap via Monte Carlo simulations
Siu A. Chin
By use of a special wave function derived from similarly transformed propagators, this work shows that the energy of a thousand spin-balanced fermions in a three-dimensional harmon…
Anatomy of Path Integral Monte Carlo: algebraic derivation of the harmonic oscillator's universal discrete imaginary-time propagator and its sequential optimization
Siu A. Chin
The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first…