On the interplay of topology and interactions: Reduced topological classification and fractional Fermi liquid

This seminar will focus on two cases where the interplay of topology and interactions allows for phases that go beyond simple quasi-particle descriptions. Both models are amenable to sign free auxiliary field quantum Monte Carlo simulations.

First, we design a two-dimensional model consisting of four Dirac-fermion layers on the square lattice. The interaction is given by a four-fermion term where each fermion is from a different layer. In the uncorrelated case, the topology is determined by a Z-valued winding number and previous studies, often using the bulk-boundary correspondence and dimensional reduction arguments, predict the reduction to a Z4 classification in the presence of correlations. An adiabatic path between formerly distinct phases has to visit a strongly interacting state that cannot be described on a mean-field level. We study the phase diagram of the full bulk system and find a symmetry broken state separating topological distinct phases. An attempt to frustrate the ordered state introduces a first order phase transition [Fig. 1 (left)].

Second, we consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a Z2 spin liquid and a fer- romagnetic phase. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the Z2 spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per unit cell, this phase is a non-Fermi liquid, also called fractionalized Fermi liquid, that violates the conventional Luttinger theorem, which relates the Fermi volume to the particle density in a Fermi liquid. We probe the Kondo breakdown in this non-Fermi liquid phase via conventional observables such as the spectral function, and also by studying the mutual information between the electrons and the spins [Fig. 1 (right)].

Figure 1: Schematic sketch of the phase diagram discussed during the beginning of the seminar (left). Numerical Results consistent with a FL* to magnetic insulator transition as subject of the second half (right).