second commit

src/hamiltonian.py

@@ -11,7 +11,7 @@ def fermi_hubbard(L:int, J:float, U:float, mu:float, w:float):
     N_down = L//2 # number of fermions with spin down
     basis = spinful_fermion_basis_1d(L,Nf=(N_up,N_down))
 
-    hop_right=[[+J*(1+w*(-1)**(i+1)),i,(i+1)] for i in range(L-1)]
+    hop_right=[[J*(1+w*(-1)**(i+1)),i,(i+1)] for i in range(L-1)]
     hop_left= [[-(J*(1+w*(-1)**(i+1))),i,(i+1)] for i in range(L-1)] 
     pot=[[-mu,i] for i in range(L-1)] 
     interact=[[U,i,i] for i in range(L)] 
@@ -29,10 +29,13 @@ def fermi_hubbard(L:int, J:float, U:float, mu:float, w:float):
     no_checks = dict(check_pcon=False,check_symm=False,check_herm=False)
     H=hamiltonian(static,dynamic,basis=basis,**no_checks) #dtype=np.float64,
     E,V=H.eigsh(k=1,which='SA',maxiter=1E10)
-    rdm=basis.partial_trace(V,sub_sys_A=([0,L-1],[0,L-1]),return_rdm="A")#,enforce_pure=False,sparse=False,subsys_ordering=True)
-    rdm2= rdm[[15,13,7,5,14,12,6,4,11,9,3,1,10,8,2,0]]
+    rdm1=Qobj(np.abs(basis.partial_trace(V,sub_sys_A=([0,L-1],[0,L-1]),return_rdm="A",enforce_pure=False,sparse=False,subsys_ordering=True)))
+    rdm2= rdm1[[15,13,7,5,14,12,6,4,11,9,3,1,10,8,2,0]]
     rdm3= Qobj(rdm2[:,[15,13,7,5,14,12,6,4,11,9,3,1,10,8,2,0]])    
     rdm3.dims=[[4,4],[4,4]]
+    #return entropy_vn(rdm1,2) #-np.matrix.trace(rdm*la.logm(rdm)/la.logm(np.matrix([[2]])))
+    #return basis.partial_trace(V,sub_sys_A=([0,1],[0,1]),return_rdm="A")
+    #return basis.ent_entropy(V,sub_sys_A=([0],[0]),return_rdm="A")['Sent_A']
     return rdm3
 
 

src/plots.py

@@ -1,8 +1,7 @@
 from hamiltonian import *
 from teleportation import *
 from concurrence import *
-from multiprocessing import Pool
-pool = Pool(processes = 20)
+import multiprocessing
 from functools import partial
 import matplotlib.pyplot as plt
 plt.rcParams.update({
@@ -13,16 +12,31 @@
 plt.rcParams['mathtext.fontset'] = 'stix'
 plt.tick_params(axis='both', which='major', labelsize=20)
 
-u=np.linspace(0.0,20,50)
-L=6
-params_list = [(L,1.0,0.0,0.0,y) for y in u]
-with Pool(processes=20) as pool:
-    b=pool.map(teleportation,params_list)
-    np.savez("/home/zakaria/QT_Fermi-Hubbard/data/fig1b_L=%s"%L,b)
-plt.plot(u,b,label=r'$L=%s$'%L)
-plt.ylabel(r'$\mathcal{F}(1,L)$',fontsize=20)
-plt.xlabel(r'$U$',fontsize=20)
-plt.legend(fontsize=20)
-plt.tick_params(axis='both', which='major', labelsize=20)
-plt.tight_layout()
-plt.savefig('/home/zakaria/QT_Fermi-Hubbard/figures/fig1b.pdf') 
+b=[]
+if __name__ == '__main__':
+    pool = multiprocessing.Pool(20)
+    J=1.0
+    mu=0.0
+    u=np.linspace(0,20,100)
+    for x in [8,10]:
+        func = partial(teleportation,x,J,mu,0)
+        b=pool.map(func,u)
+        np.savez("/home/zakaria/QT_Fermi-Hubbard/data/fig1b_L=%s"%x,b)
+        plt.plot(u,b,label=r'$L=%s$'%x)
+    plt.ylabel(r'$\mathcal{F}(1,L)$',fontsize=20)
+    plt.xlabel(r'$U$',fontsize=20)
+    plt.legend(fontsize=20)
+    plt.tick_params(axis='both', which='major', labelsize=18)
+    plt.tight_layout()
+    plt.savefig('figures/fig1b.pdf')
+
+# data=np.load("/home/zakaria/QT_Fermi-Hubbard/data/fig2c.npz")['arr_0']
+# w=np.linspace(0,0.99,50)
+# plt.plot(w,data)
+# plt.ylabel(r'$P_i$',fontsize=20)
+# plt.xlabel(r'$\delta$',fontsize=20)
+# plt.tick_params(axis='both', which='major', labelsize=15)
+# #plt.legend(fontsize=15)
+# plt.tight_layout()
+# plt.savefig('figures/fig2c.pdf')
+# plt.show()

src/teleportation.py

@@ -5,8 +5,7 @@ def u(n,m):
     op=sum(np.exp(2*np.pi*1j*k*n/d)*(fock(d,k)*fock(d,(k+m)%d).dag()) for k in range(d))
     return op
 
-def teleportation(args):
-    L,J,mu,w,U=args
+def teleportation(L,J,mu,w,U):
     d=4
     psi=sum(tensor(fock(d,r),fock(d,r)) for r in range(0,d))/np.sqrt(d) # maximaly entangled state \psi^+
     r_in=ket2dm(sum(fock(d,r) for r in range(d)).unit()) # the state to teleporte (density matrix of 1 ququart)