Hi,
I just want to say that the problem has been solved.
The original model is a spinless fermion chain as H1
----- H1 -------------
H = sum_i
- t * [ cdag_i * c_(i+1) + h.c. ]
- mu * n_i +
D * [ c_i * c_(i+1) + h.c. ]
------------------
In mps_optim, the model is transformed into a boson chain as H2
------ H2 ----------
H = sum_i
- t * [ bdag_i * b_(i+1) + h.c. ]
- mu * n_i +
- D * [ b_i * b_(i+1) + h.c. ]
----------------
where in the last line, a minus appears.
This minus does not influence the ground state energy,
since the spectrum is an even function of D, i.e., E(D) = E(-D).
Nevertheless, it
would influence the sign in the wavefunction.
For instance, with D=5, my matlab code gives the wavefunction
-----D=5--------
000: 0
001: 0.4287
010: 0.0910
011: 0
100: 0.4287
101: 0
110: 0
111: 0.7900
-------------------
On the other hand, with D=-5, my matlab code gives
----------------------
000: 0
001: -0.4287
010: 0.0910
011: 0
100: -0.4287
101: 0
110: 0
111: 0.7900
----------------------
Sun Zhao-Yu
---------- Origin message ----------
>From：comp-phys-alps-users-request@lists.phys.ethz.ch
>To：comp-phys-alps-users@lists.phys.ethz.ch
>Subject：Comp-phys-alps-users_Digest,_Vol_172,_Issue_1
>Date：2021-08-06 18:00:01
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Today's Topics:
1. about using mps_optim to simulate a p-wave superconductor.
(=?UTF-8?B?5a2Z54Wn5a6H?=)
----------------------------------------------------------------------
Message: 1
Date: Fri, 06 Aug 2021 15:15:44 +0800
From: "=?UTF-8?B?5a2Z54Wn5a6H?=" <sunzhaoyu2020@whpu.edu.cn>
To: "comp-phys-alps-users" <comp-phys-alps-users@lists.phys.ethz.ch>
Subject: [ALPS-users] about using mps_optim to simulate a p-wave
superconductor.
Message-ID: <210806151544156532004919@whpu.edu.cn>
Content-Type: text/plain; charset="utf-8"
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
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