I am trying to simulate a Spin-1 chain similar to the Bilinear Biquadratic model, of which there is a pre-built implementation in open MPS. Because it seems that it is not possible to use the symmetry of conserved total Spin \sum Sz with the Bilinear Biquadratic model, I rewrote the Hamiltonian solely in terms of Sz, S+ and S-, which are compatible with the symmetry (see attachment).
I am interested in some quantities involving Sx, such as the string correlation function Sxexp(i pi \sum Sx)Sx [site indices neglegted]. When the symmetry is enabled, one can still express this in a cumbersome way as a sum of 4 observables using S+ and S- (see attachment). My observations are the following
1) If the symmetry is enabled the results for the S+/S- version of the string correlation function can vary from simulation to simulation, sometimes making sudden jumps as a function of space. I ran the same simulation three times, using the attached bash script. (I also found sudden jumps in time, when using the TDVP).
2) If the symmetry is not enabled and I compare both expressions, the regular Sx expression seems fine, while the S+/S- version again varies from simulation to simulation.
(Parameters I used are: L=10,30,60 for AKLT-model: J=1,V=1,U=0,JJ=1/3, Heisenberg model: J=1,V=1,U=0,JJ=0, some less special point in the Haldane phase: J=1,V=1.6,U=1.25,JJ=0)
Do you know, why the two ways of expressing the string correlation function might disagree? It would be great, if it were possible to enable the symmetry and get reliable results for the S+/S- version of the string correlation function.
Hello,
I am trying to simulate a Spin-1 chain similar to the Bilinear Biquadratic model, of which there is a pre-built implementation in open MPS. Because it seems that it is not possible to use the symmetry of conserved total Spin \sum Sz with the Bilinear Biquadratic model, I rewrote the Hamiltonian solely in terms of Sz, S+ and S-, which are compatible with the symmetry (see attachment).
I am interested in some quantities involving Sx, such as the string correlation function Sxexp(i pi \sum Sx)Sx [site indices neglegted]. When the symmetry is enabled, one can still express this in a cumbersome way as a sum of 4 observables using S+ and S- (see attachment). My observations are the following
1) If the symmetry is enabled the results for the S+/S- version of the string correlation function can vary from simulation to simulation, sometimes making sudden jumps as a function of space. I ran the same simulation three times, using the attached bash script. (I also found sudden jumps in time, when using the TDVP).
2) If the symmetry is not enabled and I compare both expressions, the regular Sx expression seems fine, while the S+/S- version again varies from simulation to simulation.
(Parameters I used are: L=10,30,60 for AKLT-model: J=1,V=1,U=0,JJ=1/3, Heisenberg model: J=1,V=1,U=0,JJ=0, some less special point in the Haldane phase: J=1,V=1.6,U=1.25,JJ=0)
Do you know, why the two ways of expressing the string correlation function might disagree? It would be great, if it were possible to enable the symmetry and get reliable results for the S+/S- version of the string correlation function.
Best regards,
Sebastian