Fig. 2: Phase diagram of the one-dimensional Hubbard-Holstein model.
From: A hybrid quantum-classical method for electron-phonon systems
a, b Charge N(π) and spin S(π) structure factors for the ground state of a 6-site Hubbard-Holstein model, simulated by the non-Gaussian solver variational quantum eigensolver (NGS-VQE) algorithm as a function of u for fixed a λ = 1.5 and b λ = 3.5. The charge-density-wave (CDW) and antiferromagnetic (AFM) regimes are marked. The phonon frequency is set as ω = 10 and the quantum circuit depth is n = 9. c, d Distribution of the static c charge and d spin structure factors in the u − λ parameter plane, for the same conditions as a and b. The dashed line indicates the anti-adiabatic phase boundary u = 2λ between AFM and CDW. e Ground state infidelity and f (absolute-value) energy error with respect to ED results for the phase diagram in c and d.
