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