Variational non-gaussian approach to interacting spin-boson models

Research Approach

This paper addresses the challenge of simulating spin-boson models, where the infinite-dimensional bosonic Hilbert space and strong many-body correlations typically necessitate severe approximations. The authors propose a hybrid variational framework that avoids truncating the photonic field. Instead, they represent the bosonic sector and spin-boson correlations using a compact non-Gaussian variational manifold. The spin sector is then solved using the Density Matrix Renormalization Group (DMRG) algorithm within a self-consistent energy-minimization loop.

Methodology

The core of the approach is a variational ansatz that includes a Gaussian bosonic state (capturing displacement and squeezing) and a unitary dressing transformation. This dressing transformation is parameterized by a variational variable, λ, which allows the model to interpolate between weakly and strongly correlated regimes. By averaging the full Hamiltonian over this variational state, the authors derive an effective spin Hamiltonian. The algorithm iterates between updating the variational parameters of the bosonic sector and solving the effective spin Hamiltonian via DMRG until the total energy converges.

Main Findings and Significance

The authors benchmark their method against converged spin-boson DMRG results using the Dicke and Dicke-Ising models. They demonstrate that the hybrid approach provides accurate ground-state solutions while requiring a significantly reduced bond dimension compared to standard tensor network methods. This framework is particularly valuable for studying quantum phase transitions and collective phenomena in cavity QED and spin-phonon systems, where retaining the full bosonic degree of freedom is essential for capturing the correct physics.