The investigations of quantum many-body systems at CMSP bridges different aspects of condensed matter, statistical mechanics and quantum information. The wide spectrum of topics covered includes the study of superconductivity and magnetism in strongly-correlated systems, superfluids, cold atoms in optical lattices, localization in disordered systems, many-body physics with light, dynamics and relaxation in complex systems, quantum simulators, and quantum computing.
One of the main assumptions of statistical mechanics is that when an isolated system evolves under its Hamiltonian dynamics, it will reach a state of equilibrium where a statistical description holds. Recently, this assumption has been challenged by a series of papers demonstrating that in disordered, interacting systems, equilibration is hindered by quantum effects. This phenomenon has been dubbed Many-Body Localization (MBL) and is the subject of intense research at CMSP.
As Feynman stated in a celebrated paper, the best way to simulate a quantum system is to use another quantum system. Experimental advances in last decades, with cold atoms, trapped ions, etc, have made it possible to study the equilibrium and non-equilibrium properties of strongly correlated systems. This has revived a number of challenging theoretical questions, and we are actively working on this topic in a number of different directions at ICTP:
The properties of open quantum many-body systems were an almost unexplored area until just a few years ago. The steady state phase diagram becomes incredibly rich, displaying a variety of phenomena (novel phases and forms of order not present in equilibrium.; the universality class of the transitions may also be modified. Intense theoretical activity in this direction, has uncovered a number of unexpected features of collective behavior (including quantum synchronization) in open quantum systems. Physical systems where these phenomena can be studied include: exciton-polariton systems, arrays of coupled cavities, and Rydberg atoms. We are interested in exploring critical phenomena and exotic phases in driven dissipative systems, as well as in proposing viable setups for experimental realizations.
One of the most promising routes to building a quantum computer is the engineering of quantum annealers, or adiabatic quantum computers. While some prototypes are already being commercialized, several important theoretical and practical problems are in need of solutions. One of these is an analysis of how the adiabatic algorithm performs on classical optimization problems. Another problem is, how resilient the adiabatic computer's performance is, in the face of influence from the external environment. At CMSP we are actively working on these questions as well as in several other topics related to quantum annealing.
The goal of this research direction is to understand the fundamental physics of Fermi- and non-Fermi liquids, non-conventional superconductivity of cuprates and iron pnictides, physics of heavy-fermion compounds, properties of diluted and dense Kondo lattices, interplay between superconductivity and magnetism in strongly-correlated materials, properties of spin chains and ladders, and exotic magnetism emerging in quantum liquids. All these topics are currently under scrutiny by several members of the CMSP section.