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Here the author has done numerical calculation and has plotted energy spectrum and wave function for Kiteav Chain whose hamiltonian is given by $$H=-\mu\sum_n c_n^\dagger c_n-t\sum_n (c_{n+1}^\dagger c_n+\textrm{h.c.}) + \Delta\sum_n (c_n c_{n+1}+\textrm{h.c.})$$ I was wondering how can we also do the same using mathematica or any other tools.

Question So, for given hamiltonian how can we calculate the energy spectrum and wave function numerically?

Note: The author has used $n=35$ as lattice size.

Kartik Chhajed
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1 Answers1

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  1. Choose a basis.

  2. Write the Hamiltonian matrix in that basis (e.g. like it's done here.)

  3. Diagonalise the Hamiltonian. That will give you the eigenenergies and energy wavefunctions. On Mathematica, for instance, you'd use Eigensystem.

SuperCiocia
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