Hi, everyone,
I want to calculate the ground state of 1D p-wave superconducter, which has a Z2 symmetry,
H = sum_i - t * [ cdag_i * c_(i+1) + h.c. ] - mu * n_i + D * [ c_i * c_(i+1) + h.c. ]
My physical parameter settings are ---------------- L = 3 mu = 2 t = 1 D = 5
I have used three different methods to calculate the ground state, so as to check the reliability of the results, (1) I compile mps_optim from source with Z2 symmetry (2) I use mps_optim in anaconda without Z2 symmetry (3) I code the model with matlab in standard basis [ i.e., "empty 0" and "single-occupation 1", c|1>=|0>, cdag|0>=|1> ]
I find that (2) and (3) give the same wavefunction: --------------------- 000: 0 001: 0.4287 010: 0.0910 011: 0 100: 0.4287 101: 0 110: 0 111: 0.7900 ------------------- It indicates that (2) and (3) are using the same basis, i.e., the standard basis.
However, (1) just gives the values with extra minus sign: ---------------------- 000: 0 001: -0.4287 010: 0.0910 011: 0 100: -0.4287 101: 0 110: 0 111: 0.7900 ----------------------
Moreover, I have read the supplemental codes of this Kitaev model in the paper "Matrix product state applications for the ALPS project", i.e., the file "tsc.xml", and find that the fermion operators c and cdag are also defined in a non-standard way, which also indicates a non-standard basis:
-----------------------
<SITEBASIS name="spinless fermion"> <QUANTUMNUMBER name="P" min="0" max="1" type="fermionic"/>
<OPERATOR name="c" matrixelement="1"> <CHANGE quantumnumber="P" change="1"/> </OPERATOR>
<OPERATOR name="cdag" matrixelement="1"> <CHANGE quantumnumber="P" change="-1"/> </OPERATOR>
</SITEBASIS>
-------------------------
With this two facts, I guess mps_optim code with Z2 symmetry may use a different basis rather than the standard basis { |1>, |0> }.
Thereby, my question is that, What is the basis in the mps_optim with Z2 symmetry ? Or alternatively, what is the relation between this basis with standard basis ?
This question is quite important for extracting the true wavefunction. Any comment would be appreciated. Thank you very much.
Sun Zhao-Yu Wuhan Polytechnic University
sunzhaoyu2020@whpu.edu.cn