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tomoki.ohtsuki
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added current central charge example
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‎examples/3dBosonic.py‎

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import sage.cboot as cb
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context=cb.context_for_scalar(epsilon=0.5,Lambda=13)
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lmax=25
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nu_max=12
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cbs={}
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for spin in range(0,lmax,2):
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g=context.approx_cb(nu_max,spin)
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cbs.update({spin:g})
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def make_F(delta,spin,gap_dict):
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mat_F=context.make_F_minus_matrix(delta)
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try:
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gap=context(gap_dict[spin])
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except KeyError:
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if spin==0:
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gap=context.epsilon
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else:
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gap=2*context.epsilon+spin
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g_shift=cbs[spin].shift(gap)
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F=context.dot(mat_F,g_shift)
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return F
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def make_SDP(delta,gap_dict):
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delta=context(delta)
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Fs=[make_F(delta,spin,gap_dict) for spin in cbs.keys()]
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mat_F=context.make_F_minus_matrix(delta)
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norm=context.dot(mat_F,context.gBlock(0,0,0,0))
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obj=norm*0
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return context.SDP(norm,obj,Fs)
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from subprocess import Popen, PIPE
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import re
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sdpb="sdpb"
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sdpbparams=["--findPrimalFeasible","--findDualFeasible","--noFinalCheckpoint"]
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def bs(delta,upper=3,lower=1,sdp_method=make_SDP):
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upper=context(upper)
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lower=context(lower)
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while upper - lower > 0.001:
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D_try=(upper+lower)/2
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prob=sdp_method(delta,{0:D_try})
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prob.write("3d_Ising_binary.xml")
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sdpbargs=[sdpb,"-s","3d_Ising_binary.xml"]+sdpbparams
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out, err=Popen(sdpbargs,stdout=PIPE,stderr=PIPE).communicate()
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sol=re.compile(r'found ([^ ]+) feasible').search(out).groups()[0]
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if sol=="dual":
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print("(Delta_phi, Delta_epsilon)={0} is excluded."\
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.format((float(delta),float(D_try))))
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upper=D_try
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elif sol=="primal":
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print("(Delta_phi, Delta_epsilon)={0} is permitted."\
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.format((float(delta),float(D_try))))
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lower=D_try
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else:
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raise RuntimeError("Unexpected return from sdpb")
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return upper
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def make_SDP_for_cc(delta,gap_dict={0:1}):
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delta=context(delta)
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Fs=[make_F(delta,spin,gap_dict) for spin in cbs.keys()]
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mat_F=context.make_F_minus_matrix(delta)
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norm=context.dot(mat_F,context.gBlock(2,3,0,0))
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obj=context.dot(mat_F,context.gBlock(0,0,0,0))
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return context.SDP(norm,obj,Fs)
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def cc(delta):
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prob=make_SDP_for_cc(delta)
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prob.write("3d_Ising_cc.xml")
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sdpbargs=[sdpb,"-s","3d_Ising_cc.xml","--noFinalCheckpoint"]
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out, err=Popen(sdpbargs,stdout=PIPE,stderr=PIPE).communicate()
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sol=re.compile(r'primalObjective *= *([^ ]+) *$',re.MULTILINE)\
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.search(out).groups()[0]
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return -delta**2/float(sol)
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def make_SDP_epsilon_prime(delta,gap_dict):
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delta=context(delta)
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Fs=[make_F(delta,spin,gap_dict) for spin in cbs.keys()]
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mat_F=context.make_F_minus_matrix(delta)
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Fs+=[context.dot(mat_F,context.gBlock(0,delta,0,0))]
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norm=context.dot(mat_F,context.gBlock(0,0,0,0))
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obj=norm*0
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return context.SDP(norm,obj,Fs)
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if __name__=='__main__':
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# The default example
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#delta=0.518
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#print(bs(delta))
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# ===============================================
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# if you want to derive the central charge lower bound,
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# uncomment the follwing lines.
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#delta=0.518
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#print("central charge lower bound at delta={0} is {1}"\
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# .format(delta,cc(delta)))
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# ===============================================
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# The upper bound on epsilon' dimension.
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Delta_epsilon=0.8
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print(bs(Delta_epsilon,sdp_method=make_SDP_epsilon_prime))

‎examples/3dOn2.py‎

Lines changed: 30 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -78,13 +78,40 @@ def bs(delta,upper=3,lower=1,sector="S",sdp_method=make_SDP,NSO=2):
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raise RuntimeError("Unexpected return from sdpb")
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return upper
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def make_SDP_ccc(delta,gap_dict,NSO):
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delta=context(delta)
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pvms=[]
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for sector in ("S","T","A"):
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if sector is not "A":
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spins=[spin for spin in cbs.keys() if not spin%2]
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else:
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spins=[spin for spin in cbs.keys() if spin%2]
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for spin in spins:
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pvms.append(make_F(delta,sector,spin,gap_dict,NSO))
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norm=make_F(delta,"A",1,None,NSO,Delta=1+2*context.epsilon)
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obj=make_F(delta,"S",0,None,NSO,Delta=0)
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return context.sumrule_to_SDP(norm,obj,pvms)
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def ccc(delta,NSO=20):
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prob=make_SDP_ccc(delta,{},NSO)
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prob.write("3d_On_ccc.xml")
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sdpbargs=[sdpb,"-s","3d_On_ccc.xml","--noFinalCheckpoint"]
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out, err=Popen(sdpbargs,stdout=PIPE,stderr=PIPE).communicate()
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sol=re.compile(r'primalObjective *= *([^ ]+) *$',re.MULTILINE)\
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.search(out).groups()[0]
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return -1/float(sol)
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if __name__=="__main__":
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# The default example
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print bs(0.52)
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#print bs(0.52)
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# ======================================
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# if you want to derive the bound on Delta_T
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print bs(0.52,sector="T")
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#print bs(0.52,sector="T")
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# ======================================
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# Current central charge lowr bound for O(20)
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print ccc(0.50639,NSO=20)/2
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# Delta_phi value 0.50369 is taken from 1307.6856
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# BTW, Large N prediction for O(20) vector model is 0.9639

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