New Physics in the Complete Spectral Functions of Quantum Magnetic Models and Materials

by Dr Bruce Normand (PSI/LTC)

Tuesday 2 Dec 2025, 10:00 → 11:00 Europe/Zurich

WHGA/121

Quantum magnetic materials offer one of the best and most varied proving grounds for the combined experimental and theoretical investigation of quantum many-body problems, in particular for the study of emergent collective states and excitations. On the theoretical side, the accurate calculation of spectral functions has long been one of the biggest challenges in quantum magnetism. The understanding of entanglement as an organising principle has guided the formulation of matrix-product-state (MPS) methods as systematic variational techniques to revolutionise the quantitative numerical analysis of low-dimensional quantum magnets, affording access both to ground-state properties and, by the efficient implementation of real-time evolution, to dynamical properties.

This presentation provides an overview of selected physical results obtained recently using the intrinsically 1D method of MPS wrapped on a cylinder (cMPS), which can be applied for any local Hamiltonian, of any symmetry, including an applied magnetic field. Applying cMPS to the paradigm problem in frustrated quantum magnetism, the S = ½ triangular-lattice Heisenberg model realised in the rare-earth delafossite CsYbSe₂, benchmarks extensive scattering continua that lend themselves to an interpretation as two-magnon resonances. In the ideally frustrated “Shastry-Sutherland material” SrCu₂(BO₃)₂, the spectrum can be used to identify the leading field-induced instability as a spin-nematic phase, which is a low-field condensate formed from highly local two-magnon (S = 2) bound states.

Turning to unfrustrated Heisenberg antiferromagnets, the spectral function of the S = ½ square-lattice model reveals the presence of field-induced “shadow modes,” which are specific two-magnon bound states that have been measured in the metal-organic material (CuF₂(H₂O)₂)2pyz. The S = ½ honeycomb-lattice Heisenberg compound YbBr₃ exhibits a wide range of field-induced phenomena, including strong magnon renormalisation, progressive magnon decay, possible two-magnon binding below the saturation field and possible spinon deconfinement at low fields. While the shadow mode appears only as a broad resonance (the “magnon shadow”), the spectral function also contains a well-defined roton-like excitation at intermediate fields and Q values.

The provision of near-unbiased spectral functions for any model constitutes revolutionary progress in the field, allowing the problem of understanding the physics to be separated into two successive steps, namely “expression” and “interpretation.” An accurate expression of the spectral function at all momentum, energy and applied magnetic fields fixes the model when benchmarked against experiment, and hence refocuses attention fully on identifying the physical interpretation of their origin.