Exercise 1: Ising Model
Consider N spin-1/2 particles on a one-dimensional lattice, described by the Hamiltonian
N N−1
Hˆ = λXσzi + X σxi+1σxi,
i i
where σ’s are the Pauli matrices and λ is the interaction strength.
(a) Write a program that computes the 2N×2N matrix representation of the Hamiltonian Hˆ for different N.
(b) Diagonalize H for different N = 1,...,Nmax and λ ∈ [0 : 3]. How big is Nmax you can reach?
(c) Plot the first k levels as a function of λ for different N. Comment the spectrum.
