# How do I use iTEBD for disordered Heisenberg spin chain ( to study dynamics in Many Body Localized systems) in ITensor?

+1 vote

+1 vote
answered by (70.1k points)

Hi sayandip,
When you say iTEBD, do you mean to find the ground state or to do real-time evolution? Since you referrred to MBL, I'm assuming you mean real time evolution but I'll comment on both.

Here is a "code formula" page that shows how to make a code to do time evolution of MPS using Trotter gates, which is the best approach if you have a short ranged Hamiltonian:
http://itensor.org/docs.cgi?page=formulas/tevol_trotter

To include disorder, just define the individual Hamiltonian terms ("hterm" in the code) appropriately, with parameters depending on the bond number "b". Be careful that you use the same parameters for the reverse set of gates defined in the second loop going from N-1 down to 1.

If you pass the Gate::tReal flag as shown in the sample code, it will produce real-time evolving gates of the form exp(-i h tau). If you pass the Gate::tImag flag it will do imaginary time evolution and you can use that to project into the ground state.

But for finding the ground state, a more powerful approach is to use DMRG. Be careful, though, as DMRG can get stuck in an eigenstate which isn't the ground state if disorder is extremely strong (and depending on the initial state you give).

Best regards,
Miles

commented by (180 points)
Hey Miles thanks for the answer. I have a few more questions regarding this. How do I use this time evolution technique using two-site gates to calculate some expectation values of local operators and also correlation functions?
Also how to calculate bipartite entanglement entropy in this real-time evolution? If I do it in low disorder and high disorder limit can I expect to see the faster (t) growth vs slower growth(log t) in thermalized and localized regime respectively?
commented by (70.1k points)
Hi, so here are some resources about doing measurements and calculating entanglement entropy:
http://itensor.org/docs.cgi?page=formulas/measure_mps
http://itensor.org/docs.cgi?page=formulas/correlator_mps
http://itensor.org/docs.cgi?page=formulas/entanglement_mps

About what behavior of the entanglement entropy to expect, that depends on many things, such as the initial state you choose and details of the Hamiltonian you evolve with.