The pioneering work on geometrical frustration dates back to the 1920s, when Linus Pauling realized that the hydrogen bonds between H$_2$O molecules in ice can be allocated in multiple ways. A given oxygen atom in water ice is situated at the vertex of a diamond lattice and has four nearest-neighbor oxygen atoms, each connected via an intermediate proton according to the ice rule “two-in two-out”. Although these considerations used electric dipoles, Phil Anderson mapped them to a spin model possessing an extensive degeneracy of states. Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly these compounds are strongly correlated electrons systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we will summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates with different degrees of effective correlations. Placing organic molecules on a triangular lattice, a spin liquid ground state can be realized which allows us to investigate the genuine Mott state in the absence of magnetic order. Combining our optical data with pressure-dependent transport studies and theoretical calculations, we can construct a universal phase diagram of the correlation-controlled Mott insulator. But how important is the coupling of the fluctuating magnetic moments? How important is disorder for the electronic properties? If this resembles a quantum phase transition, is there a superconducting phase found in the vicinity and what is the superconducting glue? Can our findings be generalized, when going to a kagome or hexagonal lattice, realized in Herbert-smithites or $\alpha$-RuCl$_3$ for instance? Reference: A. Pustogow et al., Nature Materials 17, 773 (2018); Phys. Rev. Lett. 121, 056402 (2018). M. Dressel et al., J. Phys. Cond. Matter 30, 203001 (2018)
The established and highly successful description of metals is based on Landau’s Fermi liquid theory. The relevant phase space for electron-electron collisions is determined by the Pauli blocking of a degenerate Fermi gas due to its Fermi surface. In some strongly correlated systems narrow bands form and the energetics of the system at elevated energies or temperatures becomes dominated by strong interactions and is no longer restricted by Fermi-surface phase-space effects. To develop a well-controlled approach of this regime is an important question in the theory of strongly correlated electrons. In this talk I will give an overview over the description of incoherent and critical electronic systems using the Sachdev-Ye-Kitaev approach. We consider versions of the model where electrons interact with each other, with boson collective modes, and even with phonons. We also comment on the very direct relation to holographic approaches to strongly coupled quantum theories. Finally we address the emergence of superconductivity in such an incoherent metal and show that pairing and superconductivity of a fully incoherent electronic system is allowed and leads to a pairing state with high transition temperature but low condensation energy.
In quantum magnets spins form well-defined lattices and serve as model systems to study many-body quantum phases such as interacting quantum-dimer qubits, spin Luttinger-liquids, Bose glasses, or magnon Bose-Einstein condensates. Neutron, muon and photon sources are unique tools for high-precision studies of such phases, and of their correlations and excitations in as well as out of equilibrium. An overview of current frontiers in the field will be presented with special focus on recent developments in computational physics and exciting new opportunities that free electron lasers like SwissFEL and European XFEL will offer to study the time-dependence and out-of-equilibrium quantum mechanics of such systems.