# Tag Info

DMC (Diffusion Monte Carlo) Theory. Consider the Schrödinger equation in imaginary time $\tau=it$: $$-\hbar\frac{\partial\psi(x,\tau)}{\partial\tau}=\hat{H}\psi(x,\tau).$$ For a time-independent Hamiltonian $\hat{H}$, the $\tau$-dependence can be solved in a way analogous to the usual time dependence to obtain: $\psi(x,\tau)=\sum_nc_n(0)e^{-E_n\tau/\hbar}\... 10 FN-DMC (Fixed-node diffusion Monte Carlo) Theory. See my answer about DMC. The only addition for FN-DMC is that the ground state of an arbitrary Hamiltonian will not be antisymmetrized, and therefore DMC will not converge to the fermionic ground state of interest in electronic systems. To force the system to project out the fermionic ground state, then the ... 8 Magnetic Anisotropy The best way to understand magnetic anisotropy is to visualize it. I think a visualization should be co-produced with every calculation of magnetic anisotropic energy. The following figure shows Magnetocrystalline anisotropy energy calculated for G-type antiferromagnetic LiNbO3-type InFeO3$^1$. Another figure shows MAE of CuO calculated ... 7 Stochastic Series Expansion (SSE) Monte Carlo Theory: SSE is a finite-temperature, discrete-time technique that works well for quantum spin problems (e.g. Heisenberg model) and other lattice Hamiltonians in any number of dimensions. The method works by expanding the partition function in a Taylor series$\$\tag{1} Z = \mathrm{Tr}[ \rho] = \mathrm{Tr}[e^{-\...