Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

TL;DR

This paper reveals that the ferrimagnetic sawtooth chain exhibits an incommensurate quantum spin spiral, challenging previous notions of commensurate order, and employs advanced large-scale DMRG and VUMPS simulations to analyze this phenomenon.

Contribution

The study demonstrates the presence of an incommensurate quantum spin spiral in the ferrimagnetic sawtooth chain using large-scale numerical simulations, surpassing previous understanding of its magnetic order.

Findings

Identification of incommensurate spin spiral order

Long wavelength of the spiral increases with $J'$

Accurate treatment of up to 400 sites with DMRG

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 $\avg{\vec{S}_i}$, the spiral can be detected via the connected spin-spin correlations $\avg{\vec{S}_i\cdot\vec{S}_j}-\avg{\vec{S}_i}\cdot\avg{\vec{S}_j}$ 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.