Hi!
Too long, didn't read; Is there any way ALPS can be used to self-consistently determine the mean field parameters in a Schwinger boson mean field framework?
I am currently writing my masters' thesis in condensed matter physics, focusing on the possible identification of quantum spin liquids in magnetically frustrated systems. The model I am currently studying is the Kane-Mele-Hubbard model on the honeycomb lattice, which is studied in "Phys. Rev. B 85, 195126", with an additional Dzyaloshinskii-Moriya interaction (DMI) term. I treat my system in the same way as is done in the paper, employing a Schwinger boson mean field theory to obtain the mean field ground state energy from the spin Hamiltonian. The ground state energy contains both the original parameters in the Hamiltonian and some mean field parameters introduced in the mean field approximation. Having obtained the ground state, the next step is to self-consistently determine the mean field parameters numerically and construct the resulting phase diagram, which should resemble Fig. 2 in "Phys. Rev. B 85, 195126" when the DMI is set to zero. I am having some trouble determining the mean field parameters in an accurate way. The approach I have used so far is consistent with what is usually done in literature: We minimize the mean field ground state energy (assuming T=0) with respect to the mean field parameters and solve the resulting self-consistency equations for a number of initial parameter guesses, accepting as the solution that which gives the lowest value for the ground state energy. Even if the lattice is composed of 20 to 40 sites in each spatial direction, the run-time of the computation varies between 2-8 hours, and the results are inconsistent. Going to the more accurate continuum limit, where the self-consistency equations become integrals over the Brillouin zone, the run-time is so high that the approach is unreasonable. This integral approach has, however, proven successful in one dimension for a simpler initial Hamiltonian.
The question I am asking is therefore if there is an implementation in ALPS that can be used to determine these mean field parameters. I am perhaps worried that the problem I'm working on is a bit too "narrow" to be covered by ALPS, which seem to me to have excellent approaches to the more general Hamiltonians that one often starts out with (e.g. the original Kane-Mele-Hubbard model, Eq. (1) in"Phys. Rev. B 85, 195126"). If anyone has any ideas or pointers, I would be most grateful.
I apologize for the longevity of the mail and thank you in advance.
Best regards, Stein Kåre L. Fosstveit
Dear Stein,
I don’t think ALPS can do this. I’m not aware of open source code which does that, but I may be proven wrong. You can find some technical numerical details of implementation of Schwinger bosons mean-fields in here https://arxiv.org/pdf/1207.4058.pdf (But this may not apply exactly to what you are looking for)
Best regards Fabien
On 14 Mar 2022, at 21:22, Stein Kåre Lundeberg Fosstveit skfosstv@stud.ntnu.no wrote:
Hi!
Too long, didn't read; Is there any way ALPS can be used to self-consistently determine the mean field parameters in a Schwinger boson mean field framework?
I am currently writing my masters' thesis in condensed matter physics, focusing on the possible identification of quantum spin liquids in magnetically frustrated systems. The model I am currently studying is the Kane-Mele-Hubbard model on the honeycomb lattice, which is studied in "Phys. Rev. B 85, 195126", with an additional Dzyaloshinskii-Moriya interaction (DMI) term. I treat my system in the same way as is done in the paper, employing a Schwinger boson mean field theory to obtain the mean field ground state energy from the spin Hamiltonian. The ground state energy contains both the original parameters in the Hamiltonian and some mean field parameters introduced in the mean field approximation. Having obtained the ground state, the next step is to self-consistently determine the mean field parameters numerically and construct the resulting phase diagram, which should resemble Fig. 2 in "Phys. Rev. B 85, 195126" when the DMI is set to zero. I am having some trouble determining the mean field parameters in an accurate way. The approach I have used so far is consistent with what is usually done in literature: We minimize the mean field ground state energy (assuming T=0) with respect to the mean field parameters and solve the resulting self-consistency equations for a number of initial parameter guesses, accepting as the solution that which gives the lowest value for the ground state energy. Even if the lattice is composed of 20 to 40 sites in each spatial direction, the run-time of the computation varies between 2-8 hours, and the results are inconsistent. Going to the more accurate continuum limit, where the self-consistency equations become integrals over the Brillouin zone, the run-time is so high that the approach is unreasonable. This integral approach has, however, proven successful in one dimension for a simpler initial Hamiltonian.
The question I am asking is therefore if there is an implementation in ALPS that can be used to determine these mean field parameters. I am perhaps worried that the problem I'm working on is a bit too "narrow" to be covered by ALPS, which seem to me to have excellent approaches to the more general Hamiltonians that one often starts out with (e.g. the original Kane-Mele-Hubbard model, Eq. (1) in"Phys. Rev. B 85, 195126"). If anyone has any ideas or pointers, I would be most grateful.
I apologize for the longevity of the mail and thank you in advance.
Best regards, Stein Kåre L. Fosstveit
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Dear Fabien,
Thank you for your reply, and for the paper linked! Indeed, the algorithm discussed in the paper is very similar to the one I am using, and which there seems to be broad consensus about as the preferred approach in literature) There may be differences in the actual implementation though. I will keep trying! Thank you again.
Best regards Stein Kåre ________________________________ Fra: Comp-phys-alps-users comp-phys-alps-users-bounces@lists.phys.ethz.ch på vegne av Fabien Alet alet@irsamc.ups-tlse.fr Sendt: tirsdag 15. mars 2022 09:27 Til: comp-phys-alps-users@lists.phys.ethz.ch comp-phys-alps-users@lists.phys.ethz.ch Emne: Re: [ALPS-users] ALPS for Schwinger boson mean field theory?
Dear Stein,
I don’t think ALPS can do this. I’m not aware of open source code which does that, but I may be proven wrong. You can find some technical numerical details of implementation of Schwinger bosons mean-fields in here https://arxiv.org/pdf/1207.4058.pdf (But this may not apply exactly to what you are looking for)
Best regards Fabien
On 14 Mar 2022, at 21:22, Stein Kåre Lundeberg Fosstveit <skfosstv@stud.ntnu.nomailto:skfosstv@stud.ntnu.no> wrote:
Hi!
Too long, didn't read; Is there any way ALPS can be used to self-consistently determine the mean field parameters in a Schwinger boson mean field framework?
I am currently writing my masters' thesis in condensed matter physics, focusing on the possible identification of quantum spin liquids in magnetically frustrated systems. The model I am currently studying is the Kane-Mele-Hubbard model on the honeycomb lattice, which is studied in "Phys. Rev. B 85, 195126", with an additional Dzyaloshinskii-Moriya interaction (DMI) term. I treat my system in the same way as is done in the paper, employing a Schwinger boson mean field theory to obtain the mean field ground state energy from the spin Hamiltonian. The ground state energy contains both the original parameters in the Hamiltonian and some mean field parameters introduced in the mean field approximation. Having obtained the ground state, the next step is to self-consistently determine the mean field parameters numerically and construct the resulting phase diagram, which should resemble Fig. 2 in "Phys. Rev. B 85, 195126" when the DMI is set to zero. I am having some trouble determining the mean field parameters in an accurate way. The approach I have used so far is consistent with what is usually done in literature: We minimize the mean field ground state energy (assuming T=0) with respect to the mean field parameters and solve the resulting self-consistency equations for a number of initial parameter guesses, accepting as the solution that which gives the lowest value for the ground state energy. Even if the lattice is composed of 20 to 40 sites in each spatial direction, the run-time of the computation varies between 2-8 hours, and the results are inconsistent. Going to the more accurate continuum limit, where the self-consistency equations become integrals over the Brillouin zone, the run-time is so high that the approach is unreasonable. This integral approach has, however, proven successful in one dimension for a simpler initial Hamiltonian.
The question I am asking is therefore if there is an implementation in ALPS that can be used to determine these mean field parameters. I am perhaps worried that the problem I'm working on is a bit too "narrow" to be covered by ALPS, which seem to me to have excellent approaches to the more general Hamiltonians that one often starts out with (e.g. the original Kane-Mele-Hubbard model, Eq. (1) in"Phys. Rev. B 85, 195126"). If anyone has any ideas or pointers, I would be most grateful.
I apologize for the longevity of the mail and thank you in advance.
Best regards, Stein Kåre L. Fosstveit
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