Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

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 Si , the spiral can be detected via the connected spin-spin correlations Si • Sj − Si • Sj 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 L = 400 sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). This is possible due to the exploitation of the SU(2) symmetry which results in effective bond dimensions of more than 1,000,000. 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.