### The Workshop

The workshop is promoted by the Europen Science Foundation Program INSTANS and several Portuguese projects. Our main aim is to generate a lively exchange of ideas between researchers working in the different but nevertheless related fields of ultra-cold atoms, quantum information, superconductivity, and spintronics.Quantum many-body systems show a variety of striking phenomena not observed in ensembles of classical particles. Quantum interference, quantum coherence, quantum entanglement and quantum statistics - fermionic, bosonic or fractional - often conspire in producing intricate many-particle states, including macroscopically coherent phases - Bose-Einstein condensation, superconductivity, charge- and spin-density waves, to name but a few. The spectacular effects seen in transport experiments, for instance in the Quantum Hall Effect, in conductance quantization or in the Pauli blockade, also are related to the same quantum conspiracy. The aims of the workshop on "Quantum coherence and correlations in condensed-matter and cold-atom systems" will be both to elucidate the multiple facets of a very active field of research and to bridge the gaps between traditionally separate topics.

During the workshop some fundamental concepts will be introduced, such as quantum entanglement, topological order or integrability. A variety of different types of quantum matter will be considered, including cold atoms, strongly correlated electrons in transition metal oxides, graphene, quantum wires, quasi-one-dimensional compounds and quantum dots. Some phenomena will be described in detail, such as the interplay of magnetism and superconductivity in layered cuprates and pnictides, the competition of charge-density waves and superconductivity in metallo-organic chain compounds and the emergence of ferromagnetism and Mott states in fermionic systems of cold atoms. A strong emphasis will be given to recent developments in the study of quantum many-body states, for instance tensor network states and their relation to the density-matrix renormalization group, the characterization of states using string order parameters or the notion of the entanglement spectrum. A minority of talks will be rather technical, such as one on the calculation of expectation values of observables in integrable systems, another one on the mapping of spin models onto quantum-field theories. Conversely, several talks will be related to experiments exploring particularly intriguing phenomena, such as the mysterious pseudogap phase of cuprates, spin-dependent transport through double quantum dots, the existence of a quantum-critical point in some pnictides, correlation effects in bilayer graphene. Two experimentalists will present their recent measurements, on graphene and organic chain compounds, respectively.

At the end of this workshop the participants should be able to answer most of the following questions:

What is the difference between classical and quantum correlations?

What is quantum information?

What is the meaning of topological quantum computation?

What is behind the concept of integrability? Can we calculate measurable quantities of integrable systems? How?

What is so special about graphene? How can we use it for making a field-effect transistor?

What are matrix product states and how are they related to the density-matrix renormalization group? Can they be used for describing ground states of integrable systems?

How to define entanglement entropy? And what is the meaning of the entanglement spectrum? Are these concepts useful?

And what about the interplay of magnetism and superconductivity in cuprates and pnictides? Why is there a pseudogap "phase" in cuprates, but not in pnictides?

Is it correct to say that fermionic gases in optical lattices can be used for simulating the Hubbard model? In what respect the picture changes when proceeding from spin 1/2 fermions to particles with spin 5/2?

Workshops in Evora have a long tradition. The beautiful medieval town offers an ideal setting for bringing together people working in different but related fields. In the past, discussions often continued after the last session of the day and sometimes outlasted the closing hours of the bars scattered around the center of town. The month of October is an ideal period for visiting the Alentejo region, where excursions to the surroundings of Evora and its megalithic monuments can be made at moderate temperatures.

### Workshop site

Anfiteatro 131-AEdifício do Espirito Santo

Universidade de Évora