• Lea Ferreira dos Santos

  • Computer Codes

    This webpage is supported by the NSF CAREER award grant DMR-1147430. The purpose is to make available computer codes developed with postdocs and undergraduate students. You will find detailed explanations on how to use these codes, as well as illustrations and suggestions for exercises.

     
    3) Notes for the lectures given in the International Summer School on Exact and Numerical Methods for Low-Dimensional Quantum Structures that took place at the Izmir Institute of Technology, Turkey, from August 23 to August 31, 2014. The tutorial teaches how to develop computer codes to diagonalize exactly one dimensional spin-1/2 systems. In hands of the eigenvalues and eigenstates, we then: (i) analyze  signatures  of  quantum  phase  transition,  localization,  and  quantum  chaos; (ii)  investigate  the  dynamics  of  the  system by  studying   the survival probability and  the  evolution  of various  few-body  observables; (iii)  compare  the  infinite time  averages  of  observables  with  thermal  averages  and   identify   conditions  that  can  lead  to  the  thermalization  of  isolated  quantum  systems. Computer programs in Mathematica and Fortran 90 are provided. These notes will be frequently updated, so suggestions and corrections are very welcome.

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    2) Codes for the work developed with undergraduate students Kira Joel and Davida Kollmar (2012-2013)

    "An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains" (paper)

    American Journal of Physics 81, 450 (2013)

    This Mathematica code in pdf can be used to

    (i) Diagonalize the Hamiltonian matrix

    (ii) Find the density of states and Inverse Participation Ratio for all eigenstates

    (iii) Study the time evolution of different initial states

    (iv) Analyze the effects of the symmetries of the system 

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    1) Codes for the work developed with undergraduate student Aviva Gubin (2011-2012)

    "Quantum chaos: an introduction via chains of interacting spins-1/2" (new version)

    American Journal of Physics 80, 246 (2012)

    (i) Density of states, level spacing distribution and NPC for spin-1/2 chain (spin-1/2 chain Mathematica code)
    (ii) Density of states, level spacing distribution, and NPC for Gaussian Orthogonal Ensembles (GOE Mathematica code)
    (iii) NPC for 18 sites and 6 spins up (code in Fortran 77) .f in pdf
    (iv) Suggestions for exercises Extra Exercises

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