Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
This work addresses the challenge of simulating strongly correlated fermions in fields like ultracold quantum gases, condensed matter, and warm dense matter physics, offering a general and flexible method that could deliver new physical insights, though it appears incremental as it builds on existing neural canonical transformation ideas.
The paper tackled the problem of accurately simulating interacting fermions at finite temperature, particularly in low-temperature regimes where quantum Monte Carlo methods struggle due to the fermion sign problem, by developing a variational density matrix approach that provided accurate results for electrons in a two-dimensional quantum dot, demonstrating an interaction-induced crossover from Fermi liquid to Wigner molecule.
We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.