Heisenberg model dynamical correlation function via DMRG

given by Mario Collura

Term: 0

Start: 20-01-2022 End: 04-02-2022 Room: 131

Credits: 3

Schedule: Thu 9:00 - 11:00, Fri 9:00 - 11:00

Program

This hands-on course has a double aim: first, gently introducing the students to the technical aspects in developing the DMRG algorithm; second, guiding the students to apply a DMRG-based numerical iterative techniques to face with a standard problem which can be encounter in typical condensed matter setup, namely compute dynamical correlation functions.

The approach will be the following:

  1. Consider the Heisenberg Hamiltonian H with OBC and implement infinite-system DMRG algorithm to find an approximation of the ground state |GS> in the thermodynamics limit;
  2. Extending the code in such a way to be able to targetting extra states in costructing a proper reduced (renormalised) basis.
  3. Implement an efficient procedure to compute the action of the renormalised many-body operstors to a generic state in the
    DMRG basis.
  4. Then consider the operator

    S^{z}(q) = Sum_{j} \exp(i q j) S^{z}_j

     and compute the dynamical correlation function (or its Fourier transform)

    via the Green function

    < GS | S^{z}(q) (z - H)^{-1} S^{z}(q) | GS >

    using the continued fraction methods, for q = 0, pi/2 and pi.

 
References will be given during the lectures.