This project emerged within the Computational Quantum Matter group at UNC Chapel Hill and is dedicated to the automated calculation of the quantum virial expansion. The latter is a Taylor expansion that organizes the quantum many-body problem by adding one particle at a time at each successive order. In its present form, the QVEE calculates the coefficients of the expansion for non-relativistic matter with a zero-range interaction.
The ultimate goal of the QVEE is to determine the thermodynamics of non-relativistic matter, for applications to nuclear, atomic, and condensed matter physics. The specific objective is to furnish predictions of thermodynamic observables (equations of state, response, hydrodynamics) based on the specification of fermionic and bosonic degrees of freedom and their interactions.
The QVEE uses well-known expressions of the virial coefficients in terms of N-body canonical partition functions. The latter functions are then estimated using a discretization of imaginary time and a Trotter-Suzuki factorization of the transfer matrix to separate kinetic energy from interaction contributions. Automated algebra is then used to derive mathematical expressions for the canonical partition functions, which are evaluated using Gaussian integration.
This material is based upon work supported by the National Science Foundation under Grant No. PHY2013078.