[SOLVED] QIC - Computational Quantum Physics - Week 7

Description

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.

• Write a program that computes the 2^N×2^N matrix representation of the Hamiltonian H^ˆ for different N.
• Diagonalize H for different N = 1,…,N_max and λ ∈ [0 : 3]. How big is N_max you can reach?
• Plot the first k levels as a function of λ for different N. Comment the spectrum.

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