Spin-spin correlation functions for the square-lattice Heisenberg antiferromagnet at zero temperature

Cross validation in stochastic analytic continuation

Stochastic analytic continuation (SAC) of quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g., narrow peaks and divergent edges, to be resolved with unprecedented fidelity. Often it is not known what exact sharp features, if any, are present a priori, and, due to the ill-posed nature of the analytic continuation problem, multiple spectral representations may be acceptable. In this work we borrow from the machine learning and statistics literature and implement a cross validation technique to provide an unbiased method to identify the most likely spectrum among a set obtained with different spectral parametrizations and imposed constraints. We demonstrate the power of this method with examples using imaginary-time data generated by QMC simulations and synthetic data generated from artificial spectra. Our procedure, which can be considered a form of model selection, can be applied to a variety of numerical analytic continuation methods, beyond just SAC.

Spin dynamics of antiferromagnetically coupled bilayers-the case of Cr2TeO6

Understanding the dynamics of interacting quantum spins has been one of the active areas of condensed matter physics research. Recently, extensive inelastic neutron scattering measurements have been carried out in an interesting class of systems, Cr₂(Te, W, Mo)O₆. These systems consist of bilayers of Cr³⁺ spins (S  =  3/2) with strong antiferromagnetic inter-bilayer coupling (J) and tuneable intra-bilayer coupling (j) from ferro (for W and Mo) to antiferro (for Te). In the limit when [Formula: see text], the system reduces to weakly interacting quantum spin-3/2 dimers. In this paper, we discuss the low-temperature magnetic properties of Cr₂TeO₆ systems where both intra-layer and inter-layer exchange couplings are antiferromagnetic, i.e. [Formula: see text]. Using linear spin-wave theory we obtain the magnon dispersion, sublattice magnetization, two-magnon density of states, and longitudinal spin-spin correlation function.

Fractional excitations in the square lattice quantum antiferromagnet

Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.

High-energy magnon dispersion and multimagnon continuum in the two-dimensional Heisenberg antiferromagnet

We use quantum Monte Carlo simulations and numerical analytic continuation to study high-energy spin excitations in the two-dimensional S = 1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse (x) and longitudinal (z) dynamic spin structure factors Sx,z(q,omega) at q = (pi,0) and (pi/2, pi/2). Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at (pi,0) is 10% lower than at (pi/2, pi/2). We also discuss the transverse and longitudinal multimagnon continua and their relevance to neutron scattering experiments.