About the entropy growth in random unitary circuit
Posted: 20 May 2022, 02:59
I am trying to simulate the entropy growth in Random Unitary Circuit. I start from an L=8 chain and got this plot.
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?
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?
- output.png (44.76 KiB) Viewed 1883 times
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 $S$')