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Quantum spin spiral ground state of the ferrimagnetic sawtooth chain
by Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch
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Submission summary
| Authors (as registered SciPost users): | Matthias Peschke · Roman Rausch |
| Submission information | |
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| Preprint Link: | scipost_202207_00027v2 (pdf) |
| Data repository: | https://doi.org/10.24355/dbbs.084-202209231709-0 |
| Date accepted: | 2022-12-01 |
| Date submitted: | 2022-10-07 11:18 |
| Submitted by: | Rausch, Roman |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $⟨\vec{S}_i⟩$, the spiral can be detected via the connected spin-spin correlations $⟨\vec{S}_i\cdot\vec{S}_j⟩-⟨\vec{S}_i⟩\cdot⟨\vec{S}_j⟩$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.
List of changes
- data repository URL added
- new Fig. 5 added to demonstrate the local minima
- Fig. 4 switched from semilogarithmic to linear
- descriptions of the numerical procedures and tolerances are revised/rearranged
- statements on the large "effective bond dimension" are withdrawn according to criticism from report #3
- new Ref. [48] added
Published as SciPost Phys. 14, 052 (2023)
Reports on this Submission
Report
The manuscript has been sufficiently improved by addressing all of the referee's suggestions/requests. Especially, new Fig. 5 on the local minima issue and the added data repository URL are very informative for numerical researchers. As I wrote in my previous report, the findings in this paper are very interesting and give a deeper insight in to the field of low-dimensional frustrated magnets. The numerical results seem to be also reliable. Therefore, I recommend a publication of this paper in SciPost Physics.