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arXiv:2607.17934

Variational non-gaussian approach to interacting spin-boson models

João Pedro Mendonça, Yao Wang, Krzysztof Jachymski

quant-phSubmitted Jul 20, 2026• Announced Jul 21, 2026• 0 citations
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Abstract

We apply a hybrid variational framework to interacting spin-boson Hamiltonians, targeting regimes where simulations are limited by the unbounded bosonic Hilbert space and strong many-body correlations. The bosonic sector and spin-boson correlations are captured within a compact non-Gaussian variational manifold, while the minimized spin sector is obtained as the solution to an effective spin Hamiltonian. Minimization is carried out inside a self-consistent energy-minimization loop, where variational parameters are minimized and the effective Hamiltonian is solved via DMRG. The results are obtained without eliminating or truncating the photonic field. We benchmark the method on the Dicke and Dicke-Ising models by comparison to converged spin-boson DMRG, finding accurate ground-state solutions with reduced bond dimension.

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We apply a hybrid variational framework to interacting spin-boson Hamiltonians, targeting regimes where simulations are limited by the unbounded bosonic Hilbert space and strong many-body correlations. The bosonic sector and spin-boson correlations are captured within a compact non-Gaussian variational manifold, while the minimized spin sector is obtained as the solution to an effective spin Hamiltonian. Minimization is carried out inside a self-consistent energy-minimization loop, where variational parameters are minimized and the effective Hamiltonian is solved via DMRG. The results are obtained without eliminating or truncating the photonic field. We benchmark the method on the Dicke and Dicke-Ising models by comparison to converged spin-boson DMRG, finding accurate ground-state solutions with reduced bond dimension.
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.
We present a framework for simulating the open dynamics of spin-boson systems by combining variational non-Gaussian states with a quantum trajectories approach. We apply this method to a generic spin-boson Hamiltonian that has both Tavis-Cummings and Holstein type couplings and which has broad applications to a variety of quantum simulation platforms, polaritonic physics, and quantum chemistry. Additionally, we discuss how the recently developed truncated Wigner approximation for open quantum systems can be applied to the same Hamiltonian. We benchmark the performance of both methods and identify the regimes where each method is best suited. Finally, we discuss strategies to improve each technique.
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/21/21/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed.
We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an entangling transformation of photonic and atomic degrees of freedom. By truncating the resulting cavity-dressed Hamiltonian (CDH) to successively larger excitation sectors, we construct a series of compact models that converge to the exact limit, outpacing conventional approaches even in the challenging resonant and ultrastrong light-matter regime. The mapping principle also applies to multimode cavities coupled to matter through noncommuting operators and to leaky cavities. We benchmark the CDH framework on the quantum Rabi model, demonstrating accurate spectral predictions in both weak and strong coupling regimes, together with converging ground-state and thermal observables. We study the Dicke-Heisenberg lattice model and determine its phase diagram under resonant and strong light-matter coupling, achieving significant computational savings over brute-force simulations and identifying cavity-mediated spin correlations both analytically and numerically. The closed-form and compactness of the CDH provide both physical insight and enhanced computational efficiency, facilitating studies of strongly coupled hybrid light-matter systems.
The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2 S = 1 / 2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.
Explicitly correlated methods, which represent dominant short-range correlations by a diagonal Jastrow-type correlator, are designed to accurately describe systems of strongly correlated electrons, such as the fully periodic 2D Fermi--Hubbard model. However, as the reference state is compact in momentum space whereas the correlator acts naturally in real space, there is a fundamental mismatch of bases that classical algorithms resolve only by restricting the reference or the correlator. Here we propose a hybrid algorithm in which a quantum processor prepares a low-entanglement momentum-space matrix product state (MPS), precomputed classically by the transcorrelated method at the cost of a nonvariational energy, rotates it to real space, and measures in bases fixed by the Hamiltonian. Because the measurement bases are independent of the correlator, the correlator can be variationally optimized entirely in classical post-processing with no quantum-classical feedback loop. We demonstrate our algorithm on 32 qubits of Quantinuum's H2-2 with a bond-dimension-4 MPS for the half-filled 4×44 \times 44×4 lattice and achieve a relative ground-state energy error of 16±4%16 \pm 4\%16±4% after postselection, reduced to 3.5±0.5%3.5 \pm 0.5\%3.5±0.5% by calibration using low-order moments from the MPS. Compared with other feedback-free hybrid algorithms, even under generous assumptions, our method requires fewer samples than quantum-selected configuration interaction and fewer two-qubit gates than quantum Krylov methods.