Comp-phys-alps-users

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August 2021

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2 discussions

Re: [ALPS-users] about using mps_optim to simulate a p-wave superconductor [solved]
by 孙照宇 07 Aug '21

07 Aug '21

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(a)lists.phys.ethz.ch >To：comp-phys-alps-users(a)lists.phys.ethz.ch >Subject：Comp-phys-alps-users_Digest,_Vol_172,_Issue_1 >Date：2021-08-06 18:00:01Send Comp-phys-alps-users mailing list submissions to comp-phys-alps-users(a)lists.phys.ethz.ch To subscribe or unsubscribe via the World Wide Web, visit https://lists.phys.ethz.ch/listinfo/comp-phys-alps-users or, via email, send a message with subject or body 'help' to comp-phys-alps-users-request(a)lists.phys.ethz.ch You can reach the person managing the list at comp-phys-alps-users-owner(a)lists.phys.ethz.ch When replying, please edit your Subject line so it is more specific than "Re: Contents of Comp-phys-alps-users digest..." 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(a)whpu.edu.cn> To: "comp-phys-alps-users" <comp-phys-alps-users(a)lists.phys.ethz.ch> Subject: [ALPS-users] about using mps_optim to simulate a p-wave superconductor. Message-ID: <210806151544156532004919(a)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(a)whpu.edu.cn

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about using mps_optim to simulate a p-wave superconductor.
by 孙照宇 06 Aug '21

06 Aug '21

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

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