Details

Autor(en) / Beteiligte

• Javed, Umar

Titel

Universality and Phase Transitions in Nonequilibrium Boundary Dynamics

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2023

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• The intricate connection between many-body interactions and correlations serves as the fundamental basis for emergent phenomena across diverse fields like condensed matter physics, atomic and molecular physics, high energy physics, and many more. Traditionally it can be very challenging to understand the nature of correlated phases of matter in many-body extended systems using non-perturbative methods. In order to overcome these challenges, one should look for simpler models with similar complexity, and by first studying these simpler models, one can build their better understanding of emergent phenomena in extended many-body systems.A fundamental class of such systems are quantum impurity models in strongly correlated systems. These models involve the embedding of one or a few degrees of freedom in a many-body system. One unique advantage of studying these systems is that, most often in these systems, strong impurity-environment interactions can be treated exactly. Various analytical and numerical methods can be used to study the dynamics of these systems, in turn allowing a better understanding of emergent phenomena in many-body systems. Examples of emergent phenomena in many-body systems includes the Anderson orthogonality catastrophe in quantum dots and quantum impurity systems systems, transport in one-dimensional junctions with strong electron-electron interactions, the generation and growth of entanglement among magnetic impurities and their surrounding fermionic or bosonic environments.In this dissertation, our goal is to understand the novel features of quantum impurity models. Specifically, our focus lies on the many-body systems, namely one-dimensional interacting Ising chain with a strong-symmetry breaking boundary impurities.Many-body quantum systems are known to undergo phase transitions at criticality exhibiting scale-invariance and divergence of correlation lengths. Strong-symmetry breaking boundary impurities in many body systems can lead to new universality classes and new emergent phenomena not typically observed in the bulk. In classical and quantum systems the study of the effect of boundary perturbations on the critical points of extended many-body systems has been of great interest.In the first part of this dissertation we will introduce the formalism we used to study the quantum impurity models. In the second part, we will present our comprehensive numerical and analytical results on the many-body Ising model in the presence of Z2 symmetry-breaking boundary impurities. We will present the boundary dynamics and the dynamical signatures for the emergence of novel edge modes in the presence of boundary field. Further, we will present the effects of Z2 symmetry-breaking white noise on the dynamics of an open interacting Ising chain. These problems are solved using numerical tools like exact diagonalization, density matrix renormalization and analytical tools like Keldysh renormalization group and quantum field theory. Exploring the nonequilibrium behavior of the Ising chain in the presence of white noise revealing interesting non-unitary dynamics such as many body Zeno effect that is absent in equilibrium systems. Finally we will present the effect of white noise on a driven Ising chain exhibiting novel phenomena such as time crystallinity.