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.

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The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr2RuO4. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25 K. Our work demonstrates the potential of DFT+DMFT+NRG as a new computational paradigm for real-material systems to (i) directly access real-frequency properties at arbitrarily low temperatures and (ii) reveal and elucidate the intricate renormalization process that occurs during the dressing of atomic excitations by their solid-state environment.

We demonstrate that low dimensional Kondo-Heisenberg systems, consisting of itinerant electrons and localized magnetic moments (Kondo impurities), can be used as a principally new platform to realize scalar chiral spin order. The underlying physics is governed by a competition of the Ruderman-Kittel-Kosuya-Yosida (RKKY) indirect exchange interaction between the local moments with the direct Heisenberg one. When the direct exchange is weak and RKKY dominates, the isotropic system is in the disordered phase. A moderately large direct exchange leads to an Ising-type phase transition to the phase with chiral spin order. Our finding paves the way towards pioneering experimental realizations of the chiral spin liquid in systems with spontaneously broken time-reversal symmetry.

We show that the paradigmatic Ruderman-Kittel-Kasuya-Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic interimpurity distances. This phenomenon is a direct consequence of the helicity (realized, for instance, at edges of a time-reversal invariant topological insulator) and does not take place in usual (nonhelical) Luttinger liquids.

We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of fRG computations for the four-point vertex and, consequently, the self-energy. Using the X-ray-edge singularity as an example, we demonstrate numerically that solving the multiloop fRG (mfRG) flow is equivalent to solving the (first-order) parquet equations. Thus, mfRG achieves, in effect, a solution of the parquet equations while retaining all treasured fRG advantages: no need to solve self-consistent equations, purely one-loop costs, and freedom of choice for regulators.