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Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice

by Matías G. Gonzalez, Bernard Bernu, Laurent Pierre, Laura Messio

This Submission thread is now published as SciPost Phys. 12, 112 (2022)

Submission summary

As Contributors: Matías Gonzalez · Laura Messio
Arxiv Link: (pdf)
Date accepted: 2022-03-08
Date submitted: 2022-02-07 20:24
Submitted by: Gonzalez, Matías
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


The spin-$\frac12$ triangular lattice antiferromagnetic Heisenberg model has been for a long time the prototypical model of magnetic frustration. However, only very recently this model has been proposed to be realized in the Ba$_8$CoNb$_6$O$_{24}$ compound. The ground-state and thermodynamic properties are evaluated from a high-temperature series expansions interpolation method, called "entropy method", and compared to experiments. We find a ground-state energy $e_0 = -0.5445(2)$ in perfect agreement with exact diagonalization results. We also calculate the specific heat and entropy at all temperatures, finding a good agreement with the latest experiments, and evaluate which further interactions could improve the comparison. We explore the spatially anisotropic triangular lattice and provide evidence that supports the existence of a gapped spin liquid between the square and triangular lattices.

Published as SciPost Phys. 12, 112 (2022)

Author comments upon resubmission

We thank both referees for positively taking into consideration the relevance of our work, as well as for their suggestions. Below we address all of their suggestions and questions, hoping that the revised manuscript will be suitable for publication in SciPost Physics.
Yours sincerely,
The authors

List of changes

- Title updated to “Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice”

- We added the following sentence to Page 6: “We tried several scaling types and found that this one was the best. However, we do not have any microscopic argument to support it.”

- Added “For the TLHAF” to the caption of Fig. 3

- Fixed Ref. [18] and non-breaking inline formulas

- We have added the curves from Ref. [7] to our Figure 4

- Clarified the use of TLHAF in the Introduction

- We have changed the prelude of equation (5) to: “We also consider a gapped ground state with a low-temperature behavior as $c_ν(T)\sim T^2 exp(-T_0/T)$, where T_0 is the gap.”

- We have added the following explanation to Page 6: “Using three consecutive orders is a way to measure the convergence with $n$. If converged with $n$, pCPA from 3 consecutive orders will be close to the individual pCPA of a single order. Otherwise, it will be much smaller.”

- We have clarified the treatment of the singularities in the Padé Approximants at the end of Page 4 by adding: “For this function, all Padé Approximants with poles or roots in the energy range $[e_0, 0]$ are non physical and discarded directly.”

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