Dear Prof. Troyer I am trying to calculate the ground state energy of the transverse Ising-Model ( -J*4*Sx(i)*Sx(j)-h*2*Sz(i) ) on a period 1d-chain-lattice with the DMRG. Though I had use both the default model and a modified model, the results are not satisfactory. So I ask for why the DMRG doesn't give a good result in transverse field Ising model as in other 1D model. the modified model is: <MODELS> <SITEBASIS name="spin"> <PARAMETER name="local_spin" default="local_S"/> <PARAMETER name="local_S" default="1/2"/> <QUANTUMNUMBER name="S" min="local_spin" max="local_spin"/> <QUANTUMNUMBER name="Sz" min="-S" max="S"/> <OPERATOR name="Splus" matrixelement="sqrt(S*(S+1)-Sz*(Sz+1))"> <CHANGE quantumnumber="Sz" change="1"/> </OPERATOR> <OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))"> <CHANGE quantumnumber="Sz" change="-1"/> </OPERATOR> <OPERATOR name="Sz" matrixelement="Sz"/> </SITEBASIS> <BASIS name="spin"> <SITEBASIS ref="spin"> <PARAMETER name="local_spin" value="local_S#"/> <PARAMETER name="local_S#" value="local_S"/> <PARAMETER name="local_S" value="1/2"/> </SITEBASIS> <CONSTRAINT quantumnumber="Sz" value="Sz_total"/> </BASIS> <SITEOPERATOR name="Sx" site="x"> 1/2*(Splus(x)+Sminus(x)) </SITEOPERATOR> <HAMILTONIAN name="trans_Ising"> <PARAMETER name="J" default="0"/> <PARAMETER name="h" default="0"/> <BASIS ref="spin"/> <SITETERM site="i"> h*2*Sz(i) </SITETERM> <BONDTERM source="i" target="j"> J*4*Sx(i)*Sx(j) </BONDTERM> </HAMILTONIAN> </MODELS> Separately, the parameter files are: LATTICE="chain lattice" MODEL= "spin" Jz=-4 Gamma=2 local_S=1/2 SWEEPS=4 NUMBER_EIGENVALUES=1 L=8 {MAXSTATES=20} LATTICE="chain lattice" MODEL= "trans_Ising" J=-1 h=-1 local_S=1/2 SWEEPS=4 NUMBER_EIGENVALUES=1 L=8 {MAXSTATES=20}
Correspondingly, the results are: FINAL SWEEP - LAST ITERATION NUMBER OF STATES: 8 2 2 8 256 E0 = -282.636028178 ITER = 3 ENTROPY = 1.78546641552 ------------------------------------------- Truncation error = -4.98732999343e-17 ------------------------------------------- Checking if it is finished: not yet, next check in 60 seconds ( 0% done). Halted Simulation 1 This task took 46 seconds. Checkpointing Simulation 1 Finished with everything. FINAL SWEEP - LAST ITERATION NUMBER OF STATES: 8 2 2 8 256 E0 = -9.11126807853 ITER = 3 ENTROPY = 0.931162271124 ------------------------------------------- Truncation error = 2.22044604925e-16 ------------------------------------------- Checking if it is finished: not yet, next check in 60 seconds ( 0% done). Halted Simulation 1 This task took 13 seconds. Checkpointing Simulation 1 Finished with everything. but the correct data should be -10.251661790966022 which calculated by sparsediag. I don't understand why DMRG give a low precision result, even I had set h=0. Remarkably, the default model gives a wrong data, which far away from the correct one. I had exercise the XX model, which gives a very well data. I wonder if the transverse field Ising model has some special feature, or the DMRG parameter I used is not right? best regards, Shuai Cui