Quantum information dynamics in many-body systems

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The study of quantum information provides a common lens to our investigation of quantum mechanical phenomena in various fields, including condensed matter, high energy, and gravitational physics. This thesis is a collection of theoretical and numerical studies of the dynamics of quantum information in quantum many-body systems, focused on characterizing the scrambling of information and entanglement dynamics in generic dynamical setups.

In the first part of the thesis I study out-of-time-ordered correlators (OTOCs) as a probe for quantum information scrambling. By computing OTOCs in disordered quantum spin systems we find that disorder leads to distinct patterns of scrambling, and can arrest the information propagation significantly for high enough values of disorder. I also study the generic features of finite temperature OTOCs in gapped local systems and their relation to the temperature bound on chaos, using a combination of numerical and analytical approaches.

In the second part of the thesis, I study analytically tractable models of measurement-induced entanglement transition. Frequent measurements in a quantum circuit lead to distinct entanglement phases of the prepared quantum state. Using these models, we find effective field theories describing the entanglement patterns and the entanglement phase transitions. By considering generalizations of these models, we find that long-range interactions in the quantum circuit lead to novel entanglement phases with efficient emergent error-correcting properties.

In the last part of the thesis, I study tensor network states defined on generic sparse graphs. Using the intuition that generic graphs are locally tree-like, I develop efficient numerical methods to access local information of such states, which serve as a pathway for studying quantum many-body physics on sparse graphs beyond lattices.