FWF - Entanglement - Entanglement Hamiltonians in quantum many-body physics

Entanglement is one of the most fascinating features of quantum mechanics. The phenomenon of quantum entanglement refers to a particular type of correlation that is not present in the classical world. It is the most important ingredient behind the concept of quantum computation that may lead to an information technological revolution in the future. However, entanglement also plays a pivotal role in understanding the fundamental principles governing the physics of quantum many-body systems at extremely low temperatures. This realization has led to a vast effort in the research of entanglement properties in the last decades, with a particular emphasis on entanglement measures in low-dimensional systems. In simple terms, entanglement refers to the mechanism, how different parts of a many-body system are coupled in the quantum state under consideration. In a classical equilibrium setting, statistical mechanics dictates us that a small but macroscopic part of a larger total system is described by a thermal ensemble with respect to the subsystem Hamiltonian. In many-body systems at low temperatures, such as in the ground state, quantum correlations dominate over thermal ones and the description changes entirely. One could, however, still consider the state of a subsystem as a kind of thermal state with respect to the so-called entanglement Hamiltonian which is the very focus of this project. In recent years, there has been an increasing interest in the study of entanglement Hamiltonians, both on theoretical and experimental side, and a number of important features has been uncovered. In particular, in a broad class of one-dimensional ground states, the entanglement Hamiltonian of a subsystem resembles the physical Hamiltonian, albeit with a spatially varying inverse temperature. The remarkable simplicity of the entanglement Hamiltonian in the above setting raises numerous questions and opens new lines of research to explore. How does the entanglement Hamiltonian change if an inhomogeneity is present already in the physical Hamiltonian? How can one describe the crossover from the entanglement to the physical Hamiltonian when moving towards higher energies? What happens for 2D fermion systems with a non-trivial Fermi surface? What is the situation if the system is driven out of equilibrium? These are some of the main goals to be addressed in this research project.