% spising2D Hamiltonian for the 2D Ising model with aperiodic boundary condition; sparse % version. % spising2D(B,Nx,Ny) gives the Hamiltonian as a sparse matrix for the % ferromagnetic Ising model in transverse field for Nx*Ny qubits, if the % field strength is B and the coefficient % of the nearest neighbor coupling is 1. % That is, the Hamiltonian is H= - sum_k z(k) z(k+1) + B*sum_k x(k), % where x and z denote Pauli spin matrices. % The coupling is z-z and the direction of the field is x. % For the Hamiltonian aperiodic boundary condition is used. function H=spising2D(BField,Nx,Ny) x=[0 1;1 0]; y=[0 -i;i 0]; z=[1 0; 0 -1]; e=[1 0; 0 1]; % Using routines from the library to make the Ising Hamiltonian H=-splattice(z,z,Nx,Ny)+BField*spcoll(x,Nx*Ny);