Variational Multi-Gaussian Phase-Space Dynamics via Automatic Differentiation
arXiv:2507.14076
The paper presents a variational multi-Gaussian approach for simulating the dynamics of interacting open quantum bosonic systems, using a Wigner phase-space representation and automatic differentiation, and applies it to study critical behavior in a driven-dissipative 2D Bose-Hubbard lattice.
Abstract
We introduce a variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multi-dimensional Wigner phase-space representation and employs a Variational Multi-Gaussian (VMG) ansatz, whose accuracy is systematically controlled by the number of Gaussian components. The variational equations of motion are derived from the Dirac-Frenkel principle and evaluated efficiently by combining the analytical structure of Gaussian functions with automatic differentiation. As a key first physical application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses. Using our dynamical approach, we compute the finite-size scaling of the Liouvillian spectral gap, extracted from the relaxation dynamics, which vanishes in the thermodynamic limit. Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class, demonstrating the power of our method to capture complex quantum dynamics in large open systems.
PRX in press. Final version: 21 pages, 8 figures