Theoretical Solid State Physics
Our group focuses on the study of strongly correlated many particle systems, where interactions play an important role. To do so we use and develop advanced theoretical tools, in particular tensor network and functional renormalization group methods.
Current research highlights:
Projective symmetry group classification of chiral Z2 spin liquids on the pyrochlore lattice: Application to the spin-1/2 XXZ Heisenberg model
Simplified models for quantum spin-ice materials, such as the XXZ model on the pyrochlore lattice, may host interesting new spin-liquid ground states. In this work, we provide a complete classification of nearest-neighbor chiral Z2 spin-liquid states on the pyrochlore lattice using a projective symmetry group analysis. Moreover, the newly
classified states are applied to the XXZ model within a self-consistent mean-field scheme. We find a new class of spin-liquid states, the pi/3-states, that inherit their properties from fractionalization of the C3 symmetry of the pyrochlore lattice. Further, we discuss observable signatures that can be measured in neutron scattering experiments. Remarkably, the spin liquids preserve the SU(2) symmetry even in the presence of SU(2) symmetry breaking interactions.
Multipoint Correlation Functions: Spectral Representation and Numerical Evaluation &
Computing Local Multipoint Correlators Using the Numerical Renormalization Group
We show how to compute multipoint correlation functions of quantum many-body systems with unprecedented accuracy. Multipoint functions describe correlations between multiple quantum particles at different space-time points. Such functions pervade many branches of physics and are relevant for interpreting numerous types of experimental measurements, like electrical conductivities and scattering spectra of photons or neutrons. However, multipoint functions are notoriously difficult to compute, especially for strong interactions and low temperatures of interest for understanding quantum systems such as high-temperature superconductors, heavy fermions, or Hund metals.
In [F. B. Kugler, S.-S. B. Lee, and J. von Delft, Phys. Rev. X 11, 041006 (2021)], we develop a theoretical framework ("spectral representations") expressing general multipoint functions through the system's quantum states, revealing their structure with great clarity. In [S.-S. B. Lee, F. B. Kugler, and J. von Delft, Phys. Rev. X 11, 041007 (2021)], we devise a powerful method for numerically evaluating the spectral representations of local multipoint functions. With this, we compute effective two-particle interactions ("vertex functions") and, as an example, spectra for resonant inelastic x-ray scattering (RIXS), a promising experimental tool in solid-state physics. Our novel approach allows us to accurately treat energies and temperatures ranging over many orders of magnitude, beyond the reach of other numerical methods. This makes it a valuable addition to the toolbox of theoretical techniques for studying quantum matters.
Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model
Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory (DMFT), one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig’s conformal field theory (CFT) approach for multichannel Kondo models.