Strong correlations among electrons, which are caused by the Coulomb repulsion among them, induce a rich behavior of materials. Prominent examples are frustrated magnetic or unconventional superconducting states. Another example are materials which cannot be described by Fermi-liquid theory, for example, due to the strong interaction of conduction electrons with localized moments as occurs in heavy fermions systems. A more recent focus of research has been on materials such as iridium oxides where a unique combination of strong spin-orbit coupling, crystal field splitting and electron-electron correlations lead to exotic phases arising from the interplay of topology and Coulomb interactions.

## Specific research results

### Emergent criticality in the windmill lattice antiferromagnet

We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state, the spins on different sublattices are decoupled, but quantum and thermal fluctuations drive the system into a coplanar state via an “order from disorder” mechanism. We obtain the finite temperature phase diagram using renormalization group approaches.

For the same model, we perform an extensive computational experiment to test Polyakov’s conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z6 order.

[1] B. Jeevanesan, P. Chandra, P. Coleman, P. P. Orth, Phys. Rev. Lett. **115**, 177201 (2015).

[2] B. Jeevanesan, P. P. Orth, Phys. Rev. B **90**, 144435 (2014).

[3] P. P. Orth, P. Chandra, P. Coleman, J. Schmalian, Phys. Rev. B **89**, 094417 (2014). Selected as Editors’ Suggestion.

[4] P. P. Orth, P. Chandra, P. Coleman, J. Schmalian, Phys. Rev. Lett. **109**, 237205 (2012).

### Interacting topological phases of matter

Experiments of interacting cold-atomic gases in optical lattices can address outstanding open questions of condensed matter physics. One important example is the understanding and manipulation of interacting topological phases of matter. These are many-body quantum states that can only exist if both a topological band structure and strong correlations are present.

We consider interactions in the paradigmatic (time-reversal-invariant) Hofstadter-Hubbard model and a three-dimensional generalization of it. We obtain the interacting phase diagram using real-space DMFT and a (cluster) slave-rotor method. In the 3D setup we predict that by increasing the interaction strength, which is experimentally tunable, the system is driven into exotic topological Mott insulating phases.

[1] M. S. Scheurer, S. Rachel, P. P. Orth, Sci. Rep. **5**, 8386 (2015).

[2] P. P. Orth, D. Cocks, S. Rachel, M. Buchhold, K. Le Hur, W. Hofstetter, J. Phys. B: At. Mol. Opt. Phys. **46 **134004 (2013).

[3] D. Cocks, P. P. Orth, S. Rachel, M. Buchhold, K. Le Hur, W. Hofstetter, Phys. Rev. Lett. **109**, 205303 (2012).