Quantum Spins Reveal Exotic Supersolid Behaviour in Triangular Lattice Systems.

Research utilising density matrix renormalisation group and analytical methods reveals unconventional spin dynamics in the spin-1/2 XXZ model on a triangular lattice. A roton-like minimum appears in the low-energy spectrum, alongside a broad continuum, indicative of supersolid excitations and proximity to a spin liquid phase.

The behaviour of interacting quantum spins in geometrically frustrated systems continues to present a significant challenge to condensed matter physics, with potential implications for novel quantum materials. Recent experimental investigations of layered compounds have revealed intriguing evidence for supersolid phases and unconventional magnetic excitations. Researchers at the Max Planck Institute for the Physics of Complex Systems, alongside colleagues at the Technical University of Munich, have now undertaken a detailed theoretical and numerical study to elucidate these phenomena. In a paper entitled ‘Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model’, Rafael Flores-Calderón, Roderich Moessner, and Frank Pollmann combine density matrix renormalisation group calculations with analytical frameworks, including hard-core boson and variational dimer models, to characterise the low-energy spin dynamics and establish the microscopic origins of supersolid behaviour in this system. Their work provides a comprehensive analysis linking theoretical predictions to experimental observations of layered materials and offers insights into the proximity of these systems to exotic spin liquid phases.

The investigation of the spin-1/2 XXZ model on the triangular lattice, particularly under conditions of strong Ising anisotropy, reveals unconventional spin dynamics relevant to layered compounds currently under experimental scrutiny. Researchers employ a combination of large-scale numerical calculations and analytical techniques to characterise these behaviours. Density matrix renormalization group (DMRG) calculations, a numerical method used to find the ground state of quantum many-body systems, demonstrate strong agreement with data obtained from inelastic neutron scattering, a technique that probes the magnetic excitations within a material.

A key finding is the presence of a roton-like minimum in the low-energy spectrum at a specific momentum. This feature represents a dip in the energy of excitations as a function of momentum and is not predicted by traditional linear spin-wave theory, a simplified approach that treats magnetic excitations as waves. Accompanying this minimum are both peak intensity and a broad continuum of excitations at higher energies, indicating a complex interplay between quantum fluctuations, which are inherent uncertainties in quantum systems, and correlations between the spins of the electrons within the material.

Near the momentum point corresponding to the roton minimum, the spectrum exhibits approximately linear dispersion, meaning the energy of the excitations increases linearly with momentum, coupled with vanishing spectral weight, indicating a suppression of excitation intensity. This unusual behaviour suggests the emergence of novel collective modes, or coordinated movements of the spins. To interpret these observations, researchers compare two analytical frameworks. The first employs a hard-core boson approach, which maps the spin system onto an effective model of bosons, particles that mediate forces. This involves perturbation theory, an approximation technique used to solve complex problems, applied to the one-third magnetization plateau, a specific magnetic state, and a self-consistent mean-field Schwinger boson theory, a method for treating interacting bosons.

The second framework utilises a variational supersolid dimer model, which describes the system in terms of pairs of spins forming dimers, combined with a single-mode approximation, a simplification that focuses on the dominant mode of excitation. Schwinger boson theory successfully captures the broad continuum, the roton minimum, and the linear dispersion, while the dimer model reproduces the roton minimum and linear dispersion at finite momentum. Remarkably, the wavefunction derived from the dimer model and the ground state obtained from the DMRG calculations exhibit nearly identical structure factors, which describe the spatial distribution of magnetic correlations and are characterised by pronounced transverse photon-like excitations.

This convergence of theoretical and numerical results elucidates the microscopic origin of supersolid excitations, a state of matter exhibiting both crystalline order and superfluidity, within the XXZ triangular lattice model and suggests its proximity to a spin liquid phase, a state where magnetic moments are highly entangled and do not exhibit long-range order. These findings align with experimental observations and open new avenues for exploring the interplay between quantum mechanics, magnetism, and emergent phenomena in condensed matter physics.