Entanglement and bipartite fidelity in low-dimensional quantum many-body systems
(2021)
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- Authors
- Supervisors
- Hagendorf, Christian
- Abstract
- Entanglement is arguably the most puzzling yet fundamental aspect of quantum mechanics. Over the last decades, the interest in entanglement grew within various research areas, such as quantum information, high energy and condensed matter physics. In this thesis, we study entanglement in the context of quantum many-body systems in low dimensions. In 2011, Dubail and Stéphan introduced the bipartite fidelity, a measure that may be used to detect and characterise quantum phase transitions. In the first part of the thesis, we investigate this quantity in the context of critical lattice models. Using tools from quantum integrability and conformal field theory (CFT), we provide a variety of new lattice results that we compare with original CFT predictions in the context of logarithmic CFT and systems with periodic boundary conditions. In all cases, we find remarkable agreement between the CFT predictions and the lattice calculations. For systems with a global symmetry, understanding how the entanglement spreads through the various symmetry sectors is necessary to better grasp the full many-body dynamics in out-of-equilibrium situations. In the second part of the thesis, we investigate the interplay between global symmetries and entanglement in the context of quantum many-body systems out of equilibrium. In particular, we study the dynamics of symmetry-resolved entanglement measures after a global quantum quench in a one-dimensional free-fermion chain. We find exact results for the symmetry-resolved entanglement dynamics for two low-entangled initial states and provide conjectures for more generic initial states and interacting integrable models.
- Affiliations
Citations
Parez, G. (2021). Entanglement and bipartite fidelity in low-dimensional quantum many-body systems. https://hdl.handle.net/2078.5/110702