Scientific activities of the various Research Units
Status of the relevant research field; scientific context, objectives and envisaged achievements of the proposed program.
The project encompasses five interconnected research domains, namely:
1. Quantum field theories out of equilibrium.
2. Entanglement, quantum information and quantum computation
3. Low-dimensional quantum field theory, integrable models and deformations
4. Conformal invariance, conformal bootstrap and universality classes
5. Topological phases of matter, field theories and bosonization
(1) Quantum field theories out of equilibrium: A fundamental question in statistical physics is to determine the conditions under which an extended quantum system, subjected to a quench (an abrupt change of parameters in the Hamiltonian), reaches a stationary state characterized by an effective "thermal" equilibrium distribution. Conformal field theory, integrable systems, and generalized quantum hydrodynamics provide powerful methods to address this question and uncover various aspects of out-of-equilibrium dynamics. In conformal or integrable field theories, the concept of Boundary State is particularly useful as it encodes properties of the initial states and describes subsequent out-of-equilibrium dynamics. For integrable quantum field theories out of equilibrium, the presence of an infinite number of conservation laws leads to Generalized Gibbs Ensembles that better capture the long-time behavior of the system.
(2) Entanglement, quantum information and quantum computation: Entanglement measures can effectively characterize many states of matter, particularly in non-equilibrium scenarios where the traditional spontaneous symmetry-breaking description may not apply. However, the relationship between entanglement and symmetries is not fully understood yet, and will be investigated using methods of conformal field theory, AdS/CFT correspondence, topological field theory, and integrable models. Another important aspect is the study of the entanglement Hamiltonian and its modular flow as a mean to identify different topological phases of matter. Furthermore, recent experiments with cold atoms have opened up possibilities for measuring entanglement through randomized measurements and classical shadows, also promoting the development of new numerical algorithms for accessing entanglement. Extracting quantum information from many-particle systems is difficult because of the measurement postulate of quantum mechanics and the exponentially large Hilbert space. We will develop novel quantum algorithms capable of learning to classify complex quantum systems, e.g. according to their topological phase or entanglement structure, directly from measurement data.
(3) Low-dimensional quantum field theory, integrable models and deformations: Quantum integrability has proven to be a valuable tool for understanding the critical properties of quantum systems in equilibrium. The Bethe Ansatz and the associated non-linear integral equations have provided insights into the analytic structure of the free energy for many models. Exploring deformations of integrable models through irrelevant perturbations and breaking integrability has also yielded fascinating results, and the identification of new physical phenomena. These include Hagedorn-type phase transitions, connections with quantum gravity and effective string theory, confinement of topological excitations, and quantum chaotic behavior in physical amplitudes.
(4) Conformal invariance, conformal bootstrap and universality classes: Conformal field theory exactly describes the properties of strongly interacting physical systems at criticality in one and two dimensions, such as their excitations, correlation functions, and finite-size scaling. The conformal bootstrap approach allows solving theories in higher dimensions, using both numerical and analytic techniques. These have led to extremely precise determinations of critical exponents in statistical models and field theories in three and four dimensions.
(5) Topological phases of matter, field theories and bosonization: Topological phases of matter exhibit non-local coherent effects, such as long-range topological correlations (Aharonov-Bohm phases) and boundary massless excitations, without being characterized by local order parameters. These phases can be described by topological gauge theories and conformal field theories. The research in this area has gained significant momentum with the experimental observation of topological phases in insulators and semiconductors in two and three space dimensions.
