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foxqstm/MBloc toymodel.ipynb

Created May 17, 2022 11:18
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MBloc toymodel.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 45,
"id": "8670c6c9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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"(17, 18)\n",
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"EmbO -15.952872165315874\n",
"(17, 19)\n",
"Emb -35.94342081089006\n",
"EmbO -15.943420810890064\n",
"(18, 19)\n",
"Emb -35.88753217367518\n",
"EmbO -15.887532173675147\n"
]
},
{
"data": {
"image/png": 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GLw6/bzU+B7PW/SgvfEFyTRzHJ8m/osfxsm9wid/Yyxi8wvxd4CPdvHcD7571zftUt/zbwNTJxq6V/MDvMfin37eA+7qvy9bSPsx5jEtYgXIfwc/Q7wDT3fPwj8CGNZb/r4AHgfuBvwVOXaXPwSsYnCH/GHi6u3/GicaulfwrfRz75wckqUGr+Zq7JGlIlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lq0P8DkRsD/MY/ng4AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import scipy.linalg as LA\n",
"import random\n",
"import itertools\n",
"import operator\n",
"import cmath\n",
"import math\n",
"from tqdm import tqdm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"def lat_to_num(lat,L,dim):\n",
"\n",
" dd=1\n",
" num=0\n",
" for l in lat:\n",
" num+=l*L**(dim-dd)\n",
" dd+=1\n",
" return num\n",
" \n",
"def num_to_lat(num,L,dim):\n",
"\n",
" n=num\n",
" lat=[]\n",
" for d in range(dim,0,-1):\n",
" if d==1:\n",
" lat.append(n%L)\n",
" else:\n",
" dn=(n//L**(d-1))\n",
" lat.append(dn)\n",
" n-=dn*L**(d-1)\n",
" return lat\n",
" \n",
"def dist(lat1,lat2,L):\n",
" period=True\n",
" l=0\n",
" for i in range(len(lat1)):\n",
" if period:\n",
" ll=lat1[i]-lat2[i]\n",
" if abs(ll)==L-1:\n",
" ll=1\n",
" else:\n",
" ll=lat1[i]-lat2[i]\n",
" l+=(ll)**2\n",
" \n",
" return l\n",
"\n",
"def nn(lat1,lat2,L):\n",
" if dist(lat1,lat2,L)==1:\n",
" return True\n",
" else:\n",
" return False\n",
"\n",
"def AM(W,dim,L):\n",
" val=[]\n",
" for num in range(L**dim):\n",
" val.append([0]*L**dim)\n",
" for num1 in range(L**dim):\n",
" for num2 in range(num1,L**dim):\n",
" if num1==num2:\n",
" val[num1][num1]=random.uniform(-W/2,W/2)\n",
" else:\n",
" lat1=num_to_lat(num1,L,dim)\n",
" lat2=num_to_lat(num2,L,dim)\n",
"# print(num1,num2,nn(lat1,lat2,L))\n",
" if nn(lat1,lat2,L):\n",
" val[num1][num2]=-1\n",
" val[num2][num1]=-1\n",
" return val\n",
"\n",
"def mixsort2(ea,av,eb,bv):\n",
" \n",
" emin=10**5\n",
" ia=0\n",
" ib=0\n",
" e=[]\n",
" vec=[]\n",
" for i in range(len(ea)+len(eb)):\n",
" if ia<len(ea):\n",
" if ea[ia]<eb[ib]:\n",
" e.append(ea[ia])\n",
" vec.append(av[ia])\n",
" ia+=1\n",
" else:\n",
" e.append(eb[ib])\n",
" vec.append(bv[ib])\n",
" ib+=1 \n",
" \n",
" np.array(vec)\n",
" return e,vec\n",
"\n",
"def mixsort1(ea,av):\n",
" \n",
" emin=10**5\n",
" e=ea\n",
" eo=[]\n",
" vo=[]\n",
" for i in range(len(ea)):\n",
" arg=np.argmin(e)\n",
" eo.append(ea[arg])\n",
" vo.append(av[arg])\n",
" e.pop(arg)\n",
" \n",
" np.array(vo)\n",
" return eo,vo\n",
"\n",
"def mixsort(ea,av,eb,bv,cv,dv):\n",
" \n",
" emin=10**5\n",
" ia=0\n",
" ib=0\n",
" e=[]\n",
" vec=[]\n",
" eo=[]\n",
" sign=[]\n",
" for i in range(len(ea)+len(eb)):\n",
" if ia<len(ea):\n",
" if ea[ia]<eb[ib]:\n",
" e.append(ea[ia])\n",
" vec.append(av[ia])\n",
" eo.append(cv[ia])\n",
" sign.append(+1)\n",
" ia+=1\n",
" else:\n",
" e.append(eb[ib])\n",
" vec.append(bv[ib])\n",
" eo.append(dv[ib])\n",
" sign.append(-1)\n",
" ib+=1 \n",
" \n",
" np.array(vec)\n",
" np.array(eo)\n",
" return e,vec,eo,sign\n",
"\n",
"def hermitian(arr):\n",
" arr=np.array(arr)\n",
" return np.conjugate(arr.T)\n",
"\n",
"def chain(l_2d):\n",
" \n",
" return list(itertools.chain.from_iterable(l_2d))\n",
" \n",
"dim=5\n",
"L=4\n",
"W=10.0\n",
"Ne=2\n",
"Nmax=20\n",
"U=10\n",
"\n",
"#Create AM\n",
"H0=AM(W,dim,L)\n",
"H0=np.array(H0)\n",
"\n",
"#Solve one body problem\n",
"l,v=LA.eigh(H0)\n",
" \n",
"#for n in range(len(v)):\n",
"# print(v.T@v)\n",
"\n",
"#iv=LA.inv(v)\n",
"#print(iv@a@v)\n",
"\n",
"#print('eigvec',v)\n",
"#print('eigval',l)\n",
"\n",
"#copy to spin-1/2\n",
"vup=[]\n",
"vdown=[]\n",
"for vec in v:\n",
" vup.append(vec)\n",
" vdown.append(vec)\n",
" \n",
"#degeneracy problem\n",
"Hsp=[]\n",
"for i in range(len(vup)):\n",
"# print(cc)\n",
" Uij=0\n",
" for j in range(len(vup[i])): \n",
" Uij+=vup[i][j]*U*vdown[i][j]\n",
" \n",
" Hsp.append([[0,Uij],[np.conjugate(Uij),0]])\n",
"Hsp=np.array(Hsp)\n",
"\n",
"#Solve the degeneracy\n",
"lspup=[]\n",
"vspup=[]\n",
"lspdown=[]\n",
"vspdown=[]\n",
"lsoup=[]\n",
"lsodown=[]\n",
"for i,h in enumerate(Hsp):\n",
"# print('h',h)\n",
" a,b=LA.eigh(h)\n",
" lspup.append(l[i]+a[0])\n",
" lsoup.append(l[i])\n",
" vspup.append(v[i]*(b[0][0]+b[0][1]))\n",
" lspdown.append(l[i]+a[1])\n",
" lsodown.append(l[i])\n",
" vspdown.append(v[i]*(b[1][0]+b[1][1]))\n",
"#print('Etest',Etest)\n",
"#print('lspup',lspup)\n",
"#print('lspdown',lspdown)\n",
"\n",
"#print('lspdown',lspdown)\n",
"#print('lspup',lspup)\n",
"\n",
"#Sort eigenvalue and eigenvectors\n",
"be,bv,bo,sign=mixsort(lspup,vspup,lspdown,vspdown,lsoup,lsodown)\n",
"\n",
"c=list(itertools.combinations(list(range(Nmax)),Ne))\n",
"print(len(c))\n",
"\n",
"#Create excited state basis\n",
"c=list(itertools.combinations(list(range(Nmax)),Ne))\n",
"mbv=[1]*len(c)\n",
"Emb=[0]*len(c)\n",
"EmbO=[0]*len(c)\n",
"spin=[[]]*len(c)\n",
"for i,cc in enumerate(c):\n",
" for j in cc:\n",
" mbv[i]*=bv[j]\n",
" Emb[i]+=be[j]\n",
" EmbO[i]+=bo[j]\n",
" spin[i].append(sign[j])\n",
" \n",
"for i,cc in enumerate(c):\n",
" print(cc)\n",
"# print('spin',spin[i])\n",
" print('Emb',Emb[i])\n",
" print('EmbO',EmbO[i])\n",
"\n",
"Emb.sort()\n",
" \n",
"dE=[]\n",
"for i in range(len(c)-1):\n",
" dE.append(Emb[i+1]-Emb[i])\n",
"\n",
"dE=len(dE)*dE/sum(dE) \n",
"\n",
"plt.figure()\n",
"plt.hist(dE,bins=20,density=True)\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.11"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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