Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

Abstract

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.

11 pages, 6 figures, code: https://github.com/buwantaiji/FermiFlow

References in corpus (16)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Theory of ultracold Fermi gases
• Determinantal point processes for machine learning
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Sliced Score Matching: A Scalable Approach to Density and Score Estimation
• Structure of fermion nodes and nodal cells
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
• Fermionic quantum criticality and the fractal nodal surface
• Inferring the quantum density matrix with machine learning
• The Expressive Power of a Class of Normalizing Flow Models
• Exchangeable Neural ODE for Set Modeling
• Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo
• Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits

Cited by in corpus (15)

• Ab-initio quantum chemistry with neural-network wavefunctions
• First principles simulations of dense hydrogen
• Deep Variational Free Energy Approach to Dense Hydrogen
• Free energy calculation of crystalline solids using normalizing flow
• $m^{\ast }$ of two-dimensional electron gas: a neural canonical transformation study
• Neural canonical transformations for vibrational spectra of molecules
• Training models using forces computed by stochastic electronic structure methods
• Abnormal superfluid fraction and structural properties of electrons in 2D and 3D quantum dots: an ab initio path-integral Monte Carlo study
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Quantum Anharmonic Effects in Hydrogen-Bond Symmetrization of High-Pressure Ice
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Deep generative modelling of canonical ensemble with differentiable thermal properties
• Neural Canonical Transformations for Quantum Anharmonic Solids of Lithium
• Neural Canonical Transformation for the Spectra of Fluxional Molecule CH5+