A grand challenge for the quantum materials field is the development of tools to experimentally measure, certify and quantify entanglement and quantum correlations in real materials. Such tools are needed in order to identify materials suitable to novel applications in Quantum Information Science (QIS), including quantum computing and sensing. In addition, many intriguing quantum states of matter are theoretically understood—or even defined—in terms of their entanglement properties. However, entanglement entropies and density matrices are not directly accessible in macroscopic materials, so new methods are needed for the identification of such phases.

Together with inelastic neutron scattering colleagues, we have thus worked to develop model-independent ways to experimentally detect and quantify entanglement in materials using spectroscopic experiments. By making use of quantum Fisher information (QFI) and other entanglement witnesses—observables that serve as order parameters for a subset of entangled states—we showed that the S = 1/2 isotropic Heisenberg antiferromagnetic chain KCuF3 features at least quadpartite entanglement at the lowest temperatures and bipartite entanglement up to at least 150 K. We also investigated the S = 1/2 transverse-field XXZ chain Cs2CoCl4, finding tripartite entanglement at low fields, and showing how these witnesses provide new insight into quantum phase transitions. For both quantum spin chains, we find excellent agreement between experiment and simulations of the INS spectra using the density matrix renormalization group (DMRG). Recently, such witnesses have been used to help diagnose quantum spin liquid states.

We have also theoretically considered the Hubbard chain as a first extension to electronic (i.e. spinful fermionic) systems. This is an important but nontrivial step since quantum information methods are typically designed for two-level systems. We have also defined a family of spatial quantum correlation functions, and extracted a new length scale, the quantum coherence length, from KCuF3 neutron data. In a related approach, we look at the information contained in real-time real-space correlation functions in 1D quantum spin systems and the Hubbard chain.

We have a review of this exciting and rapidly growing multidisciplinary field, arXiv:2405.10899.

We are interested in understanding and predicting the effects of correlations in quantum materials. In pursuit of this goal, we use complementary theoretical and numerically exact unbiased many-body techniques, such as DMRG, exact diagonalization (ED), and thermal pure quantum state (TPQ) methods, with an aim to achieve quantitative modeling and understanding of realistic systems beyond phase diagrams and ground state properties, enabling close comparisons with experiment.

In this area, we have worked on a variety of systems:

• the Kitaev spin liquid candidate 𝛼−RuCl3 using ab initio, ED and TPQ, and machine learning methods.

• the related honeycomb antiferromagnet YbCl3 

• the triangular-lattice quantum spin liquid NaYbSe2

• quantum spin chains, including KCuF3, Cs2CoCl4, Sr2V3O9, and the generalized quantum spin compass chain.

• one-orbital and two-orbital Hubbard chains

• other models of relevance to superconductors

Going forward, we are particularly interested in pursuing methods for calculating accurate dynamical structure factors for large two- and three-dimensional systems.

Topological states of matter have been one of the most important and influential directions in condensed matter physics over the past 50 years. It has led to the introduction of new paradigms, and was recognized through the 2016 Physics Nobel prize. A younger field within this umbrella is that of topological magnetic excitations, which seeks to combine topology and strong electron-electron interactions.

Our work in this field includes the first discovery of an extensive 2D magnon nodal-plane degeneracy in elemental gadolinium, Physical Review Letters 128, 097201 (2022), Physical Review B 105, 104402 (2022), one of the few elemental ferromagnets. We also made early predictions of topological magnons with nonzero Chern numbers in noncollinear antiferromagnets such as pyrochlore iridates and kagome antiferromagnets, leading to a magnon thermal Hall effect.

We are also interested in developing analytical methods — both exact and approximate. These offer a different path to understanding interacting many-body systems, as well as ways to ensure the accuracy of our computational tools. Using a renormalization group-like flow equation formalism, we developed a method to generate highly accurate time-evolution operators for periodically driven (Floquet) many-body systems. Unlike conventional high-frequency expansions, our method is non-perturbative and allows access to the low-frequency regime in dynamic quantum matter. As a related result we developed a Hamilton-Jacobi formalism for the time-evolution operator that provides a unified framework for these approximation methods. In a more recent work we were able to use flow equations to derive nonperturbative approximations to operator square-roots even where Taylor expansions fail, and to obtain a resummed version of the Holstein-Primakoff spin representation.