Each bond is less than ln(2)=0.69, 2*ln(2)=1.39, 3*ln(2)=2.08 and 4*ln(2)=2.77 plateaus at late times.

(I have roughly 0.625, 1.30, 1.87, and 2.24)

What cause this phenomenon? Is that because an ideal maximally mixed state (which is associated with the maximally entangled state) is hard to be created by a total random dynamics?

Code: Select all

```
L = 8
spin_half = SpinHalfSite(conserve='None')
psi = MPS.from_product_state([spin_half]*L, ["up", "down"]*(L//2), bc='finite')
print(psi.chi)
TEBD_params = dict(N_steps=1, trunc_params={'chi_max':100})
evo = RandomUnitaryEvolution(psi, TEBD_params)
evo.run()
print(psi.chi)
def measurement(evo, data):
keys = ['t', 'entropy', 'Sx', 'Sz', 'corr_XX', 'corr_ZZ', 'trunc_err']
if data is None:
data = dict([(k, []) for k in keys])
data['t'].append(evo.evolved_time)
data['entropy'].append(evo.psi.entanglement_entropy())
data['Sx'].append(evo.psi.expectation_value('Sigmax'))
data['Sz'].append(evo.psi.expectation_value('Sigmaz'))
data['corr_XX'].append(evo.psi.correlation_function('Sigmax', 'Sigmax'))
data['trunc_err'].append(evo.trunc_err.eps)
return data
data = measurement(evo, None)
while evo.evolved_time < 30.:
evo.run()
measurement(evo, data)
plt.plot(data['t'], np.array(data['entropy']))
plt.xlabel('time $t$')
plt.ylabel('entropy $S$')
```