Author : Joseph C. Szabo
Release : 2022
Genre : Condensed matter
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Novel Transport in Quantum Phases and Entanglement Dynamics Beyond Equilibrium by : Joseph C. Szabo

Download or read book Novel Transport in Quantum Phases and Entanglement Dynamics Beyond Equilibrium written by Joseph C. Szabo. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and identifying quantum phases have been longstanding pursuits in the field condensed matter physics. The most exciting modern problems lie at the intersection of strong correlations and quantum information where highly entangled phases of matter are the most difficult to solve both analytically and computationally. The overarching aim of this thesis is to advance our understanding of strongly correlated materials in light of advanced, microscopic measurement techniques, capable of imaging and manipulating single qubits and measuring fascinating physics such as quantum entanglement. We begin our study with the Fermi-Hubbard model, a theoretical model that captures the insulating and conducting phases of high-temperature superconducting materials, and we end our discussion by characterizing novel quantum phases and dynamics realized on cutting-edge quantum simulation platforms. Our first focus is on the repulsive Fermi-Hubbard model. We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites, while the electronic bond conductivity increases. We propose that these metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Our results provide one of the first microscopic investigations of dynamical response and how these two phases (correlated metal and Mott insulator) coexist microscopically and lead to an overall macroscopic phase transition. Our work provides novel predictions for electron conductivity measured via local microwave impedance combined with charge and spin local spectroscopies. Expanding beyond the ground state properties of interacting matter, revolutionary quantum simulation experiments provide access to new regimes of quantum matter such as dynamical transitions and steady states in nonequilibrium conditions. This allows us to explore the most mind-boggling properties of interacting quantum systems: entanglement. In our first venture exploring the field of nonequilibrium quantum dynamics, we bridge foundational atomic, molecular, and optical (AMO) and condensed matter models. We investigate competing entanglement dynamics in an Ising-spin chain coupled to an external central ancilla qudit. In studying the real-time behavior following a quench from an unentangled spin-ancilla state, we find that the ancilla entanglement entropy tracks the dynamical phase transition in the underlying spin system. In this composite setting, purely spin-spin entanglement metrics such as mutual information and quantum Fisher information (QFI) decay as the ancilla entanglement entropy grows. We define multipartite entanglement loss (MEL) as the difference between collective magnetic fluctuations and QFI, which is zero in the pure spin chain limit. MEL directly quantifies the ancilla's effect on the development of spin-spin entanglement. One of our central results is that we find MEL is proportional to the exponential of entanglement entropy in real-time. Our results provide a platform for exploring composite system entanglement dynamics and suggest that MEL serves as a quantitative estimate of information entropy shared between collective spins and the ancilla qudit. Our results present a new framework that connects physical spin-fluctuations, QFI, and bipartite entanglement entropy between collective quantum systems. We reduce the qudit/bosonic environment to a single (central) qubit as to investigate the scrambling capacity added by a simple c-qubit. We present the novel ring-star Ising model as a bridge between fast-slow scrambling: a locally interacting spin-1/2 system uniformly coupled to a central qubit vertex. Each spin becomes next-nearest neighbor to all others through the c-qubit, where stronger central coupling continuously degrades any sense of locality and achieves effective all-to-all interactions. Meanwhile, the central qubit adds two level structure to all previous eigenstates in the spectrum. We study operator and entanglement dynamics in a nonintegrable ring-star, spin-1/2 Ising model with tunable central spin coupling. As the interaction with the c-spin increases across all sites, we find a surprising transition from super-ballistic scrambling and information growth to continuously restricted sub-ballistic entanglement and increasingly inhibited operator growth. This slow growth occurs on intermediate timescales that extend exponentially with increasing coupling, indicative of logarithmic entanglement growth. We provide exact dynamics of small systems working with non-equilibrium, effective infinite temperature states, and additionally contribute analytic early-time expansions that support the observed rapid scrambling to quantum Zeno-like crossover. Finally, we apply the properties of entanglement to highlight numerically approximate methods for simulating quantum and semiclassical systems. When entanglement slowly develops locally, tensor network methods allow for efficient simulation of the minimal Hilbert space required to store the quantum wavefunction evolving under Schrodinger dynamics or quantum operators under Heisenberg evolution. In the limit of long-range interactions, the system is increasingly semiclassical where the wavefunction spreads rapidly, but the full quantum Hilbert space approaches proximate conservation of collective observables. Here we review tensor network and semiclassical numerical algorithms and provide a brief discussion on applying them to simulate the quench dynamics of the Heisenberg model. We highlight the regimes where we expect them to be accurate and the intermediate regions where the two become approximate from different limits on the range of interaction.