**Emergent quantum phenomena - ****More is different!**

**More is different!**

## Quantum magnetic-structural phase transitions with trapped ions |
"More is different" in quantum physics, an observation made by Nobel prize winner P. W. Anderson. The properties of physical systems of many particles may be complex, but they often show emerging regular patterns that can be understood in terms of the underlying symmetries and universality classes. We have predicted the emergence of intriguing phenomena in trapped ion quantum simulators, such as a phase transition between a normal and superfluid phase that is driven by strong spin-phonon interactions.
D. Porras, P.A. Ivanov, F. Schmidt-Kaler, Physical Review Letters 108, 235701 (2012). P. Nevado, D. Porras, Physical Review A 93, 013625 (2016). |

## Gauge symmetry in spin-boson chains |
Gauge symmetry is a key concept in high energy physics. A system posses a gauge symmetry when its properties are unchanged by a local transformation. In condensed matter systems, a local (gauge) symmetry can appear when an external field is replaced by a quantum field with its own dynamics. In trapped ion or superconducting qubit chains, a gauge symmetry can be induced by using auxiliary degrees of freedom provided by vibrations or photonic modes. We have predicted that spin-boson models with gauge symmetries show a complex phase diagram with an exotic first order phase transition. Whereas we have been able to describe the ground state, still many interesting questions regarding the dynamics of this system remain open.
P. Nevado, D. Porras, Physical Review A 92, 013624 (2015). |