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Commit 350826ac authored by Donjan Rodic's avatar Donjan Rodic
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Merge branch 'master' of gitlab.phys.ethz.ch:compphys_lectures/cqp_fs16

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exercises/ex04_solution/heised_python/heised.ipynb 0 → 100644
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%% Cell type:code id: tags:
``` python
import numpy as np
import scipy.sparse.linalg as LA
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = 16, 9
```
%% Cell type:code id: tags:
``` python
class Heisenberg:
def __init__(self,L,nup,periodic=False,j=1.):
self.L = L
self.nup = nup
self.periodic = periodic
self.j = j
self.index = -np.ones((1<<self.L),dtype=int)
states = []
## find all basis states with given nup
i = 0
for s in range((1<<nup)-1,len(self.index)):
if bin(s).count('1')==self.nup:
self.index[s] = i
states.append(s)
i+=1
self.states = np.array(states,dtype=int)
self.N = len(self.states)
def multiply(self,x):
assert(len(x)>=self.N)
y = np.zeros_like(x)
# diagonal part
for i,s in enumerate(self.states):
jtotal = 0.
for r in range(self.L-1):
jtotal += -1 if ((s >> r)^(s >> (r+1)))&1 else 1
y[i] = 0.25*self.j*jtotal*x[i]
# off-diagonal part
for i,s in enumerate(self.states):
for r in range(self.L-1):
if ((s >> r)^(s >> (r+1)))&1 :
sflipped = s^(3 << r)
y[self.index[sflipped]] += 0.5*self.j*x[i]
if self.periodic:
for i,s in enumerate(self.states):
y[i] += 0.25*self.j*(-1 if (s^(s >> (self.L-1)))&1 else 1)*x[i]
if (s^(s >> (self.L-1)))&1 :
sflipped = s^(1|(1 << (self.L-1)))
y[self.index[sflipped]] += 0.5*self.j*x[i]
return y
```
%% Cell type:markdown id: tags:
# Test Energies
%% Cell type:code id: tags:
``` python
E_o = []
E_p = []
Lmin = 2
Lmax = 12
for L in range(Lmin,Lmax):
nup = L//2
heis_o = Heisenberg(L,nup,periodic=False)
H = LA.LinearOperator( (heis_o.N,heis_o.N), matvec=heis_o.multiply)
w,_ = LA.eigsh(H, 1, which='SA')
E_o.append(w/L)
heis_p = Heisenberg(L,nup,periodic=True)
H = LA.LinearOperator( (heis_p.N,heis_p.N), matvec=heis_p.multiply)
w,_ = LA.eigsh(H, 1, which='SA')
E_p.append(w/L)
plt.figure()
plt.plot(1/np.arange(Lmin,Lmax),E_o,label='open')
plt.plot(1/np.arange(Lmin,Lmax),E_p,label='periodic')
plt.xlim([1/Lmax,1/Lmin])
plt.title('Ground state energy per site')
plt.xlabel('$1/L$')
plt.ylabel('$E_0/L$')
plt.legend()
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
```
exercises/ex06_solution/pimc.ipynb 0 → 100644
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