23.1 derivative operator

an other possibility will be to take derivatives of the correlator $$\nabla_t^2\langle\tilde \phi(t)\tilde \phi(0) \rangle$$ in this case however we do not know how to define a GEVP.

Defining the derivative operator $$\nabla_+ \tilde\phi(t)=\tilde\phi(t+1)-\tilde\phi(t)$$ we can construct the GEVP $$\begin{pmatrix} \langle\tilde{\phi_0}(t)\tilde{\phi_0}(0) \rangle & \langle\tilde{\phi_0}(t)\tilde\phi_0^3(0) \rangle & \langle\tilde{\phi_0}(t)\tilde{\phi_1}(0) & \langle\tilde \phi_0(t)(-\nabla_-) \tilde\phi_0(0) \rangle \rangle \\ & \langle\tilde{\phi_0}^3(t)\tilde{\phi_0}^3(0) \rangle & \langle\tilde{\phi_0}^3(t)\tilde{\phi_1}(0) \rangle &\langle\tilde{\phi_0}^3(t)(-\nabla_-)\tilde{\phi_0}(0) \rangle \\ & & \langle\tilde{\phi_1}(t)\tilde{\phi_1}(0) \rangle & \langle\tilde{\phi_1}(t)(-\nabla_-)\tilde{\phi_0}(0) \rangle\\ &&& \langle \nabla_+\tilde{\phi_0}(t)(-\nabla_-)\tilde{\phi_0}(0) \rangle \end{pmatrix}$$ notice that $$\langle \nabla_+\tilde{\phi_0}(t)(-\nabla_-)\tilde{\phi_0}(0) \rangle = \langle\tilde{\phi_0}(t+1)\tilde{\phi_0}(-1) \rangle -\langle\tilde{\phi_0}(t+1)\tilde{\phi_0}(0)\\ -\langle\tilde{\phi_0}(t)\tilde{\phi_0}(-1) \rangle-\langle\tilde{\phi_0}(t)\tilde{\phi_0}(0) \rangle\\ =c(t+2)-2c(t+1)+c(t)$$ does not really help in the GEVP

23.1.0.1 ../../g0.25/out/G2t_T64_L24_msq0-4.868000_msq1-4.710000_l02.500000_l12.500000_mu5.000000_g0.250000_rep0_output

GEVP_phi0_phi03_phi1_meffl0(L24T64) = 0.132949(60) $\chi^2/dof=$ 0.016036

GEVP_phi0_phi03_phi1_meffl1(L24T64) = 0.426617(85) $\chi^2/dof=$ 1.2008

GEVP_phi0_phi03_phi1_meffl2(L24T64) = 0.43759(42) $\chi^2/dof=$ 192.02

GEVP_0_3_1_d0_meffl0(L24T64) = 1 $\chi^2/dof=$ -nan

GEVP_0_3_1_d0_meffl1(L24T64) = 0.133004(56) $\chi^2/dof=$ 0.094397

GEVP_0_3_1_d0_meffl2(L24T64) = 0.42666(13) $\chi^2/dof=$ 0.28956

GEVP_0_3_1_d0_meffl3(L24T64) = 0.44173(38) $\chi^2/dof=$ 88.047

d0d0_meff(L24T64) = 0.17705(33) $\chi^2/dof=$ 123.37