Variational study of the neutron resonance mode in the cuprate superconductors

A Gutzwiller-type variational wave function is proposed for the neutron resonance mode in the cuprate superconductors. An efficient reweighting technique is devised to perform variational Monte Carlo simulation on the proposed wave function which is composed of linearly superposed Gutzwiller projected Slater determinants. The calculation, which involves no free parameter, predicts qualitatively correct behavior for both the energy and the spectral weight of the resonance mode as functions of doping.

Figure 1

The resonance energy determined from the single-mode approximation as a function of doping. The inset shows the structure factor at $Q=\left(\pi ,\pi \right)$ (divided by the number of lattice sites, $N_s$) as a function of doping.

Figure 2

(Color online) The optimized variational parameters as a function of doping.

Figure 3

(Color online) The optimized pairing parameters as a function of doping and the off-diagonal long-range order calculated from the variational ground state.

Figure 4

(Color online) The spin-fluctuation spectrum at $q=\left(\pi ,\pi \right)$ as a function of excitation energy and doping determined from the variational calculation. The calculation is done on a $14\times 14$ lattice. The delta function peaks of the spectrum are broadened into Lorentzian peaks with a width of $0.1t$.

Figure 5

(Color online) The mode energy determined by our variational approach as a function of doping as compared with the result of SMA.

Figure 6

The relative spectral weight of the resonance mode as a function of doping. The inset shows the result of the absolute spectral weight.