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Unfrustrating the t-J Model: Exact d-wave BCS Superconductivity in the t'-J_z-V Model

by Kevin Slagle

Submission summary

As Contributors: Kevin Slagle
Arxiv Link:
Date accepted: 2019-10-01
Date submitted: 2019-08-03
Submitted by: Slagle, Kevin
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Condensed Matter Physics - Theory
Approach: Theoretical


The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a t'-J_z-V model on a square lattice, which has a second-nearest-neighbor hopping t' (instead of a nearest-neighbor hopping t), an Ising (instead of Heisenberg) antiferromagnetic coupling J_z, and a nearest-neighbor repulsion V. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.

Ontology / Topics

See full Ontology or Topics database.

Ising model Superconductivity/superconductors

Published as SciPost Phys. 7, 046 (2019)

Submission & Refereeing History

Submission 1906.06344v1 on 3 August 2019

Reports on this Submission

Anonymous Report 1 on 2019-9-29 Invited Report

  • Cite as: Anonymous, Report on arXiv:1906.06344v1, delivered 2019-09-29, doi: 10.21468/SciPost.Report.1202


This work introduces a new, physically motivated, member of the t-J-V type models and solves it. In the analytical solution of this system, superconductivity appears naturally along with antiferromagnetism. Very few models display the ease with which this is derived here. I think that it is very refreshing to see a new model with such controlled results.

Although the title contains the word "exact", the calculations invoke the (standard BCS) mean-field approximation (Appendix B) as well as analysis (in Appendix A) in various limit which enable analytical results. I think that it would be better to replace that word by something else.

As the author wrote, a possible weakness might be that only next-nearest-neighbor hopping is allowed. However, that is indeed very well physically motivated noting early works. Indeed, the dispersion relation for a single hole in an antiferromagnetic background may indeed display only harmonics associated with next nearest neighbor hopping. An illuminating work where this is further made lucid is

E. Louis, F. Guinea, M. P. L´opez Sancho, and J. A. Verg´es, Phys. Rev. B 59, 14005 (1999).

This dominant nearest neighbor hopping in an antiferromagnetic background was employed, in the past, to motivate kinetically driven stripe formation and pairing.

With the removal of the nearest neighbor hopping, the new t'-J_{z}-V model of the author is quite remarkable in the ease in which many results follow.

I strongly recommend the publication of this work with the possible minor change regarding the wording of the title.

  • validity: top
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  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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