To understand the intricated behavior of quantum systems of many constituents is one of the main aims of modern physics. This is because they exhibit a wide range of interesting and exotic phenomena with no parallel in classical physics, including phase transitions at zero temperature, superconductivity, or topological effects. Yet, the very same complexity that is responsible for the rich physics is at the same time a road block in their study. The dimension of Hilbert space, so the configuration space of quantum mechanics, scales exponentially with the system size, rendering naive methods often inapplicable.
In this seminar, we will make an attempt to obtain an overview over modern approaches to the study of quantum systems with many constituents. This will concern both analytical approaches as well as numerical ones, ranging from density-matrix renormalization over tensor network approaches to ideas of holographic states to describe quantum fields. We will have a look at simulating quantum lattice models with ultra-cold atoms in optical lattices and will address questions of non-equilibrium.
Nov. 9: Entanglement theory.
Nov. 16: Area laws.
Nov. 23: Density-matrix renormalization (DMRG).
Nov. 30: Matrix-product states.
Dec. 14: Time-dependent DMRG.
Jan. 11: Lieb-Robinson bounds and quantum cellular automata.
Jan. 18: Exact state transfer in quantum spin chains
Jan. 25: Quantum fields and continuous matrix product states.
Feb. 18: Keldysh formalism.
Feb. 8: Hamiltonian complexity.
Feb. 15: Quantum error correction.
Feb. 22: Topological order and topological entanglement entropy.
Leitung: Jens Eisert
Uebung: Robert Huebener, Thomas Barthel, Vincent Nesme, Mathis Friesdorf, Matthias Ohliger, Alexander Kegeles, Brian Tarasinski, Janina Gertis.
Ort und Zeit der Vorlesung: Taeglich zwischen 10:00 und 13:00, grosser Hoersaal, Arnimallee 22.
Ort und Zeit der Uebung: Taeglich zwischen 14:00 und 17:00, in Raeumen der Arnimallee 14. Die Liste der Raeume ist hier zu finden.