## Loschmidt Echo

How do I use this algorithm? What does that parameter do?
Mike
Posts: 2
Joined: 15 Sep 2020, 08:16

### Loschmidt Echo

Hi Johannes/everyone,
I am trying to perform some sudden quench simulations in the transverse field 1D Ising model and compute the Loschmidt echo. I am doing everything based on the nice example code "c_tebd.py" that is already provided. The procedure that I pursue is the following:
I first set the initial state of the system to the ground state of TFI chain with no coupling (J=0) by MPS:

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model_params = dict(L=L, bc_MPS='finite', conserve=None, verbose=verbose)
M_0 = TFIChain(model_params)
p_state = ["up"] * M_0.lat.N_sites
psi_0 = MPS.from_product_state(M_0.lat.mps_sites(), p_state, bc=M_0.lat.bc_MPS)

Now, I want to see how the initial state psi_0 evolves under the dynamics of the 1D Ising Hamiltonian with J=1. To generate the model I use

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model_params = dict(L=L, J=1., g=g, bc_MPS='finite', conserve=None, verbose=verbose)
M_1 = TFIChain(model_params)

Then, without changing the 'tebd_params' I set

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eng = tebd.Engine(psi_0, M_1, tebd_params)
l_echo = [abs(eng.psi.overlap(psi_0))/psi_0.norm/eng.psi.norm]
Nstep = int(tmax / dt_measure + 0.5)
for n in range(Nstep):
eng.run()
l_echo.append(abs(eng.psi.overlap(psi_0))/psi_0.norm/eng.psi.norm)
But I only get a flat line at 1, which is not what one would expect. So, am I doing anything wrong?
Best,
Mike
Johannes
Posts: 207
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

### Re: Loschmidt Echo

Welcome!

The MPS which you pass to the TEBDEngine gets modified in place (because we want to avoid unnecessary copies of MPS in case they are large).
In other words, psi_0 and eng.epsi are the same MPS (namely the time evolved one).

The solution is to make a copy of the MPS at some point, e.g.

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psi_0 = MPS.from_product_state(M_0.lat.mps_sites(), p_state, bc=M_0.lat.bc_MPS)
psi_t = psi_0.copy()
...
eng = tebd.Engine(psi_t, M_1, tebd_params)

Mike
Posts: 2
Joined: 15 Sep 2020, 08:16

### Re: Loschmidt Echo

Thanks Johannes!
It indeed worked.