Theory
Perhaps more than any other area of solid state physics, in quantum magnetism experiment goes hand in hand with theory. It is always hard to say "who started it." This is particularly true for neutron scattering, which quantitatively measures exactly the same spin correlation functions that theorists like to calculate. The theoretical models that describe quantum magnetism and find real-world incarnations in our materials are usually of a very high degree of mathematical sophistication. We are obviously not "professional" theorists but we are very good at collaborating with such. Occasionally we even dabble in theoretical calculations ourselves.
A wonderful collaboration is with the group of Prof. Batista at the University of Tennessee. It concerns the "spin supersolid" phase of the triangular lattice antiferromagnet K2Co(SeO3)2, an exotic state of matter that is simultaneously "solid" and "superfluid" in its magnetic degrees of freedom. Here theory took the form of large-scale quantum Monte Carlo simulations, and the outcome was agreement with our thermodynamic and neutron scattering data on the quantitative level (see figure). Such extraordinary agreement is valuable far beyond bragging rights: it validates the fundamental physical interpretation of what we actually measure. For more details see M. Zhu, Leandro M. Chinellato, V. Romerio, N. Murai, S. Ohira-Kawamura, Christian Balz, Z. Yan, S. Gvasaliya, Yasuyuki Kato, C. D. Batista, A. Zheludev, Wannier states and spin supersolid physics in the triangular antiferromagnet K2Co(SeO3)2 , npj Quantum Materials 10, 74 (2025); arXiv:2412.19693.
Numerical modeling of the thermodynamics of the spin supersolid K2Co(SeO3)2. Left: magnetization measured at 190 mK (circles) compared to quantum Monte Carlo simulations (red squares). Note that linear spin wave theory (blue line) fails entirely. Right: magnetic specific heat in several applied fields: experiment (circles) against the same simulations (squares). Arrows mark the magnetic ordering transition.
The story did not end there. Theorists can sometimes find exciting physics in our data that we completely missed ourselves. Batista and co-workers predicted that in the field-induced magnetization-plateau phase this material should host two-magnon bound states , showing up only as extremely weak spectral features well above the main magnon band. We did not need any new measurements: it was enough to very carefully re-analyze the data we already had, in precisely the energy range that theory suggested. The bound states were there! For more details see Hao Zhang, Tianyue Huang, Allen O. Scheie, Mengze Zhu, Tao Xie, N. Murai, S. Ohira-Kawamura, A. Zheludev, Andreas M. Läuchli, Cristian D. Batista, Nonperturbative semiclassical spin dynamics for ordered quantum magnets , npj Quantum Mater. (2026); arXiv:2508.21142.
Theorists can also recognize new physics in experimental results that we would ourselves dismiss as "unexplained." That is exactly what happened in our work with Prof. Mila's group at EPFL. He realized that some very peculiar features in our inelastic neutron data on the spin ladder material BPCB represent a novel field-induced magnon bound state. We then worked very closely to quantitatively compare our scattering results with numerical Density Matrix Renormalization Group (DMRG) calculations. For more details see M. Nayak, D. Blosser, A. Zheludev, F. Mila, Magnetic-Field-Induced Bound States in Spin-1/2 Ladders , Phys. Rev. Lett. 124, 087203 (2020); arXiv:1912.01576.
Interactions with theorists sometimes help us design the right experiment, and occasionally even talk us into buying new equipment. Our student Daniel Flavián discovered a very prominent dielectric anomaly in the quantum magnet Cs2Cu2Mo3O12. We had no idea what it was. We started a dialog with Dr. Pavel Volkov, at the time at Rutgers University in the group of Prof. Chandra, who kept suggesting new measurements to narrow down what we were dealing with. At some point it became clear to him that the puzzle could not be cracked without frequency-dependent data. Our capacitance bridge operated at a single fixed frequency only, and he set about convincing us to invest $40,000 in a variable-frequency instrument. We finally caved in, bought it, and did the measurement. The mystery was solved: the electric dipoles in the crystal relax by exchanging energy with individual magnons , whose energy is tuned by the applied magnetic field and collapses at a quantum critical point. For more details see D. Flavián, Pavel A. Volkov, S. Hayashida, K. Yu. Povarov, S. Gvasaliya, Premala Chandra, A. Zheludev, Dielectric Relaxation by Quantum Critical Magnons , Phys. Rev. Lett. 130, 216501 (2023); arXiv:2302.04234.
The measurements that solved the mystery: real (left) and imaginary (right) parts of the complex capacitance of Cs2Cu2Mo3O12, measured in magnetic fields from 0 to 14 T (color coded), together with fits to a single relaxation model (black lines). Triangles mark the relaxation temperature T*.
Sometimes the underlying model is simply too complicated to understand the experimental data without a direct comparison with numerics. In the frustrated triangular-lattice magnet Cs2CoBr4 we discovered a spectacular hierarchy of bound spinon pairs, a "Zeeman ladder" (the measured spectrum is shown on our research pages). The trouble is that the actual material involves at least five distinct exchange couplings and fully anisotropic XYZ interactions: no analytical treatment stood a chance. In a recent collaboration with the group of Prof. Giamarchi at the University of Geneva, a minimal model of frustrated XYZ triangular spin ladders was distilled from all that complexity, and its dynamic structure factor was computed with numerically exact time-dependent matrix product state techniques. The calculation reproduces the measured spectrum in all essential detail (see figure) and shows that spinon bound states are far more robust than previously thought, surviving well beyond the strongly Ising-anisotropic regime where they were first predicted. For more details see C.-M. Halati, V. Romerio, P. Steffens, J. R. Stewart, A. Zheludev, T. Giamarchi, Zeeman Ladders in Frustrated XYZ Spin Chains , arXiv:2508.17834.
Dynamic spin structure factor of Cs2CoBr4. Left: the frustrated XYZ triangular spin ladder model, computed by time-dependent matrix product state methods. Right: the spectrum measured by unpolarized neutron spectroscopy. The calculation reproduces the entire Zeeman ladder of spinon bound states.
Not all theory is numerical, though. Data can often be confronted with analytical calculations, even if evaluating the final expressions may still require taking a few integrals numerically. A recent example is our work with Prof. Chernyshev at the University of California, Irvine on K2Mn(SeO3)2, an almost-Heisenberg S = 5/2 triangular lattice antiferromagnet. Alongside conventional spin waves, this material shows a broad high-energy continuum of magnetic excitations. Non-linear spin wave theory, an analytical expansion in powers of 1/S that takes magnon-magnon interactions into account, reproduces both features with rather striking accuracy, precisely where the standard linear theory fails (see figure). For more details see M. Zhu, V. Romerio, D. Moser, K. Yu. Povarov, R. Sibille, R. Wawrzynczak, Z. Yan, S. Gvasaliya, A. L. Chernyshev, A. Zheludev, Dynamics and thermodynamics of the S = 5/2 almost-Heisenberg triangular lattice antiferromagnet K2Mn(SeO3)2 , Phys. Rev. B 113, 184436 (2026); arXiv:2602.11983.
Magnetic excitation spectra of K2Mn(SeO3)2 in zero field. Left: neutron data measured at 0.2 K. Center: linear spin wave theory, which captures the sharp magnon branches but produces no continuum. Right: non-linear spin wave theory: both the magnons and the high-energy continuum are accurately reproduced.
Sometimes our own contribution to even the purely theoretical aspects of a project is not negligible. A case in point is a wonderful collaboration with Prof. Giamarchi on finite-temperature dynamics of quantum spin chains near saturation. His pioneering finite-temperature DMRG calculations helped make sense of our neutron scattering results on the K2CuSO4Cl2 material. We are very proud that the semi-analytical calculations in this study were done by our student Dominic Blosser. He was able to evaluate the space-time correlation function of hard-core bosons in one dimension at a finite temperature (see below). For more details see D. Blosser, N. Kestin, K. Yu. Povarov, R. Bewley, E. Coira, T. Giamarchi, A. Zheludev, Finite-temperature correlations in a quantum spin chain near saturation , Phys. Rev. B 96, 134406 (2017); arXiv:1707.05243. This result was later applied in our work on finite-temperature dynamical scaling at the z=2, d=1 field-induced quantum critical point in the spin ladder BPCB: D. Blosser, V. K. Bhartiya, D. J. Voneshen, A. Zheludev, z=2 quantum critical dynamics in a spin ladder , Phys. Rev. Lett. 121, 247201 (2018); arXiv:1806.10392.
And sometimes we do theory with little to no support from "professionals" at all. Some time ago we developed a mapping of a partially depleted quantum spin ladder onto a random spin chain with no depletion but sign-alternating interactions. We then used direct diagonalization to compute the properties of this effective model, for comparison with experiments on the depleted spin ladder material DIMPY and with Quantum Monte Carlo (QMC) simulations: D. Schmidiger, K. Yu. Povarov, S. Galeski, N. Reynolds, R. Bewley, T. Guidi, J. Ollivier, A. Zheludev, Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder , Phys. Rev. Lett. 116, 257203 (2016); arXiv:1603.00070. More recently we returned to the same problem with a new question: what happens to such defects when the ladder is driven into a gapless Tomonaga-Luttinger liquid state by a strong magnetic field? Combining our own QMC simulations, analytical calculations, and an extensive calorimetric survey of depleted DIMPY and BPCB, we showed that non-magnetic defects endow the otherwise scale-free liquid with a new characteristic length L, the average distance between them. The critical staggered susceptibility then obeys a universal scaling law in the single variable LT (see figure). For more details see S. Galeski, K. Yu. Povarov, D. Blosser, S. Gvasaliya, R. Wawrzynczak, J. Ollivier, J. Gooth, A. Zheludev, LT Scaling in Depleted Quantum Spin Ladders , Phys. Rev. Lett. 128, 237201 (2022); arXiv:2111.08464.
Universal LT scaling of the critical staggered susceptibility in spin ladders, from our own quantum Monte Carlo simulations with the coupling constants of DIMPY and BPCB. Left: finite ladder segments of length L. Right: randomly depleted ladders, where L is the average distance between defects. In both cases the data collapse onto the same scaling law; dashed lines mark the infinite-system limit. Insets show the unscaled data.