Running ED simulation
As en axample of sparse Exact diagonalization method we will obtain a triplet gap as function of system size for spin chain model.
First step we need to import required packages
import pyalps
import matplotlib.pyplot as plt
import pyalps.plotPrepare the input parameters and write them into a specific format
parms = []
for l in [4, 6, 8, 10, 12, 14, 16]:
for sz in [0, 1]:
parms.append(
{.
'LATTICE' : "chain lattice",.
'MODEL' : "spin",
'local_S' : 1,
'J' : 1,
'L' : l,
'CONSERVED_QUANTUMNUMBERS' : 'Sz',
'Sz_total' : sz
}
)
#write the input file and run the simulation
input_file = pyalps.writeInputFiles('parm2a',parms)for all parameters run an sparsediag application
res = pyalps.runApplication('sparsediag',input_file)Extract the ground state energies over all momenta for every simulation
for sim in data:
l = int(sim[0].props['L'])
if l not in lengths: lengths.append(l)
sz = int(sim[0].props['Sz_total'])
all_energies = []
for sec in sim:
all_energies += list(sec.y)
min_energies[(l,sz)]= np.min(all_energies)Make a plot of the triplet gap as function of system size
gapplot = pyalps.DataSet()
gapplot.x = 1./np.sort(lengths)
gapplot.y = [min_energies[(l,1)] -min_energies[(l,0)] for l in np.sort(lengths)]..
gapplot.props['xlabel']='$1/L$'
gapplot.props['ylabel']='Triplet gap $\Delta/J$'
gapplot.props['label']='S=1'
gapplot.props['line']='.'
plt.figure()
pyalps.plot.plot(gapplot)
plt.legend()
plt.xlim(0,0.25)
plt.ylim(0,1.0)
pars = [fw.Parameter(0.411), fw.Parameter(1000), fw.Parameter(1)]
f = lambda self, x, p: p[0]()+p[1]()*np.exp(-x/p[2]())
# we fit only a range from 8 to 14
fw.fit(None, f, pars, np.array(gapplot.y)[2:], np.sort(lengths)[2:])
x = np.linspace(0, 1./min(lengths), 100)
plt.plot(x, f(None, 1/x, pars))
plt.show()The final result should look like
