Universität zu Köln

Ladewig, Björn (2023). Non-equilibrium universality: slow drives, measurements and dephasing. PhD thesis, Universität zu Köln.

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Abstract

The behavior of quantum systems can be influenced by factors such as unitary evolution, measurements or decoherence. For large composite systems, these mechanisms can give rise to collective phenomena like phase transitions and universality. One example are quantum phase transitions in the ground states of a Hamiltonian. Close to the transition scale invariant behavior emerges, characterized by a set of universal critical exponents. If the system is driven in the vicinity of the transition, the drive scale can lead to a breakdown of the equilibrium scaling behavior. Nevertheless, the breakdown inherits universal properties and gives access to the leading critical exponents (Kibble-Zurek mechanism). However, the whole hierarchy of critical exponents, relevant and irrelevant, is accessible by a slow drive. We establish this generalized mechanism and its observable consequences at the level of elementary, but experimentally relevant, spin and fermion models. We construct drives that turn equilibrium irrelevant couplings into relevant drive couplings with an observable scaling in the excitation density. Criticality and universality also arise from competing unitary evolution and measurements, allowing for measurement-induced transitions. An example are (free) fermion models featuring a transition between an extended `critical' phase and a `pinned', weakly entangled phase. We investigate the role of dephasing/imperfect measurements onto the transition based on (i) numerical approaches (stochastic quantum trajectories), (ii) an effective bosonic replica field theory, and (iii) a perturbative treatment of the fermion dynamics. On the one hand, weak dephasing leaves the `critical' phase and measurement-induced transition in tact. On the other hand, we observe the emergence of a new, temperature-like scale for strong dephasing and weak measurements, enabled by the interplay of all three mechanisms. Despite the presence of the finite scale, observables like density-dependent correlations still feature scale invariant behavior. Paired with a perturbative treatment for strong dephasing, this behavior hints at a diffusion-like dynamics on the diagonal of the density matrix in the occupation number basis.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Ladewig, Björn UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-653941
Date:	2023
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Measurement-induced transitions English Quenches English Open quantum systems & decoherence English Kibble-Zurek mechanism English
Date of oral exam:	13 February 2023
Referee:	Name Academic Title Diehl, Sebastian Prof. Dr. Rosch, Achim Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/65394