## Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

SciPost Phys. 14, 052 (2023) · published 28 March 2023

- doi: 10.21468/SciPostPhys.14.3.052
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### 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 $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ 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.

### Cited by 1

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Roman Rausch, -
^{2}^{3}^{4}Matthias Peschke, -
^{3}Cassian Plorin, -
^{5}Jürgen Schnack, -
^{1}Christoph Karrasch

^{1}Technische Universität Braunschweig / Braunschweig University of Technology^{2}Universiteit van Amsterdam / University of Amsterdam [UvA]^{3}Universität Hamburg / University of Hamburg [UH]^{4}Delta Institute for Theoretical Physics [Delta ITP]^{5}Universität Bielefeld / Bielefeld University