Problems in Mix-D model

[hyang]

I want to do calculations on the Mix-D model. For example, a bilayer t-J model with no interlayer hopping, but with interlayer spin-spin interaction. Then I define a new t-J site, with 3 conservation numbers (Nt,Nb,Sz). When I am running the DMRG with this new t-J site, I found the result is very different from the result with the original t-J site but without t_\perp. The main difference I found is that when I am increasing the bond dimension, the entanglement entropy stops growing upto some value of chi in the new t-J site, but it still grows in the original t-J site. And the energy difference is very small.


The new t-J site is defined as

Python: Select all

class t_Jk_Site(Site):

    def __init__(self, cons_N='N', cons_Sz='Sz',Ly=1,k=1):
        if cons_N not in ['N', 'parity', None]:
            raise ValueError("invalid `cons_N`: " + repr(cons_N))
        if cons_Sz not in ['Sz', 'parity', None]:
            raise ValueError("invalid `cons_Sz`: " + repr(cons_Sz))

        d = 3
        states = ['holon', 'up', 'down']
        N_diag = np.array([0,1,1], dtype=np.float64)
        Nup = np.array([0,1,0], dtype=np.float64)
        Ndown = np.array([0,0,1], dtype=np.float64)
        Ntot = np.diag(N_diag)

        JW = np.diag(1. - 2. * N_diag)  # (-1)^Nu
        JWu = np.diag(1. - 2. * Nup)  # (-1)^Nu
        JWd = np.diag(1. - 2. * Ndown)  # (-1)^Nu

        Cu = np.zeros((d, d))
        Cu[0, 1] = 1.
        Cdu = np.transpose(Cu)

        Cd_noJW = np.zeros((d, d))
        Cd_noJW[0, 2] = 1.
        Cd = np.dot(JWu, Cd_noJW)
        Cdd = np.transpose(Cd)

   
        Sz = np.zeros((d, d))
        Sz[1, 1] = 0.5
        Sz[2, 2] = -0.5

        Sp = np.zeros((d, d))
        Sp[1, 2] = 1.0

        Sm = np.zeros((d, d))
        Sm[2, 1] = 1.0


        ops = dict(JW=JW,Cu=Cu, Cdu=Cdu, Cd=Cd, Cdd=Cdd,
                   Ntot=Ntot,Sz=Sz, Sp=Sp, Sm=Sm)  # yapf: disable

        # handle charges
        qmod = []
        qnames = []
        charges = []
        M=[[0,0,0],[0,1,1]]
        if cons_N == 'N':
            for i in range(Ly):
                qnames.append('N'+str(i))
                qmod.append(1)
            for i in range(Ly):
                if i==k:
                    charges.append(M[1])
                else:
                    charges.append(M[0])
        elif cons_N == 'parity':
            for i in range(Ly):
                qnames.append('N'+str(i))
                qmod.append(2)
            for i in range(Ly):
                if i==k:
                    charges.append(M[1])
                else:
                    charges.append(M[0])
        if cons_Sz == 'Sz':
            qnames.append('Sz')
            qmod.append(1)
            charges.append([0, 1, -1])
        print(charges)
        if len(qmod) == 0:
            leg = npc.LegCharge.from_trivial(d)
        else:
            if len(qmod) == 1:
                charges = charges[Ly]
            elif len(qmod) == Ly: #need to transpose
                list1=[]
                for i in range(len(charges[0])):
                    list2=[]
                    for j in range(len(charges)):
                        list2.append(charges[j][i])
                    list1.append(list2)
                charges = list1
            else: #need to transpose
                list1=[]
                for i in range(len(charges[0])):
                    list2=[]
                    for j in range(len(charges)):
                        list2.append(charges[j][i])
                    list1.append(list2)
                charges = list1
            chinfo = npc.ChargeInfo(qmod, qnames)
            print(charges)
            leg_unsorted = npc.LegCharge.from_qflat(chinfo, charges)
            # sort by charges
            perm_qind, leg = leg_unsorted.sort()
            perm_flat = leg_unsorted.perm_flat_from_perm_qind(perm_qind)
            self.perm = perm_flat
            # permute operators accordingly
            for opname in ops:
                ops[opname] = ops[opname][np.ix_(perm_flat, perm_flat)]
            # and the states
            states = [states[i] for i in perm_flat]

        self.cons_N = cons_N
        self.cons_Sz = cons_Sz

        Site.__init__(self, leg, states, **ops)

        # specify fermionic operators
        self.need_JW_string |= set(['Cu', 'Cdu', 'Cd', 'Cdd'])

    def __repr__(self):
        """Debug representation of self"""
        return "t_Jk_Site({cN!r}, {cS!r})".format(
            cN=self.cons_N, cS=self.cons_Sz)