## How to use random MPS to acess all ground states

How do I use this algorithm? What does that parameter do?
lww
Posts: 10
Joined: 09 Jan 2019, 13:27

### How to use random MPS to acess all ground states

Hi, I was trying to obtain the two topologically degenerate ground states (easily distinguished by the symmetry of entanglement spectrum) of the lattice model detailed in arXiv:1208.2623. According to the paper (also the published version), we have roughly equal chance to obtain each of these two states if a random initial MPS is provided to the iDMRG simulation.

I created the random initial state by follwing code, each time ran the simulation with different seeds, but it always converged to the ground state in vacuum sector. I tried this method many times but never converged to the semion sector. In contrast, I can readily obtain the semion sector using 2pi flux insertion. So my question is how to adjust the tenpy code to access semion sector using random MPS.

Code: Select all

def randomize_MPS(psi, steps=6, chi=100, seed=None):
"Create a charge conserved random MPS from a product state by random unitary evolution"
np.random.seed(seed)
options = dict(N_steps=steps, trunc_params={'chi_max':chi})
RandomUnitaryEvolution(psi, options).run()
psi.canonical_form()

Johannes
Posts: 316
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

### Re: How to use random MPS to acess all ground states

Since you apply 6 steps of randomizing, it might still have some "memory" of the initial state.
This function takes an initlal MPS, I guess you take an initial product state. Did you try using another one?

It's not completely clear to me what initial states the authors of arXiv:1208.2623 took, just saying "random MPS" does not fully specify what ensemble you consider...

By the way, I'm not sure if you saw it, but TeNPy has a tenpy.models.haldane.BosonicHaldaneModel as well, although with slightly different terms, and an example using it. That probably doesn't answer your question, though.
lww
Posts: 10
Joined: 09 Jan 2019, 13:27

### Re: How to use random MPS to acess all ground states

Thanks, Johannes. By the way, what are your common practices to obtain the complete set of topologically degenerate ground states in tenpy? I know some states can be obtained by adiabatic flux insertion, but other states with non-Abelian statistics (e.g. arXiv:1412.8115) cannot be obtained in this way. Can you share some experiences?