Noncollinear phase of the antiferromagnetic sawtooth chain

Abstract

The antiferromagnetic sawtooth chain is a prototypical example of a frustrated spin system with vertex-sharing triangles, giving rise to complex quantum states. Depending on the interaction parameters, this system has three phases, of which the gapless non-collinear phase (for strongly coupled basal spins and loosely attached apical spins) has received little theoretical attention so far. In this work, we comprehensively investigate the properties of the non-collinear phase using large-scale tensor network computations which exploit the full SU(2) symmetry of the underlying Heisenberg model. We study the ground state both for finite systems using the density-matrix renormalization group (DMRG) as well as for infinite chains via the variational uniform matrix-product state (VUMPS) formalism. Finite temperatures and correlation functions are tackled via imaginary- or real time evolutions, which we implement using the time-dependent variational principle (TDVP). We find that the non-collinear phase is characterized by a low-momentum peak and a diffuse tail for the apex-apex correlations. Deep into the phase, the pattern sharpens into a peak indicating a 90-degree spiral. The apical spins are soft and highly susceptible to external perturbations; they give rise to a large number of gapless magnetic states that are polarized by weak fields and cause a long low-temperature tail in the specific heat. The dynamic spin-structure factor exhibits additive contributions from a two-spinon continuum (excitations of the basal chain) and a gapless peak at $k=\pi /2$ (excitations of the apical spins). Small temperatures excite the gapless states and smear the spectral weight of the $k=\pi /2$ peak out into a homogeneous flat-band structure. Our results are relevant, e.g., for the material atacamite Cu${}_2$Cl(OH)${}_3$ in high magnetic fields.

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• From density-matrix renormalization group to matrix product states
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Magnetocaloric effect in one-dimensional antiferromagnets
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Flat-band physics in the spin-1/2 sawtooth chain
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain

Cited by in corpus (4)

• Atacamite Cu${}_2$Cl(OH)${}_3$ in High Magnetic Fields: Quantum Criticality and Dimensional Reduction of a Sawtooth-Chain Compound
• Ferromagnetic Order of Reduced Magnetic Moments in a Frustrated Sawtooth Chain of the Magnetic Semiconductor ZnYb${}_2$S${}_4$
• Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism
• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain