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(a)whpu.edu.cn