Bridging the Gap: Local Models and Efficient Braiding for Fractional Quantum Hall on Lattices

Erscheinungsjahr 2024
ISBN: 978-3-384-25460-3
Verlag: tredition

Buch, Englisch, 136 Seiten, Paperback, Format (B × H): 155 mm x 234 mm, Gewicht: 243 g

Low dimensional, interacting quantum many-body systems host a wealth of interesting phenomena ranging from quantum phase transitions at zero temperature to topological order. The physics of such systems are often described by their ground states that are special and occupy a rather tiny fraction of the Hilbert space. These small set of low energy states have little entanglement compared to the states that live in the middle of the spectrum. In this context, the most sought after are the topologically ordered systems which are characterized by ground states with speci?c degeneracy on a manifold, long range entanglement and excitations that obey fractional statistics known as anyons [1]. The classic example is the fractional quantum Hall (FQH) effect, which is a phase induced when a 2D gas of interacting electrons is subject to large magnetic ?elds [2, 3].
Interestingly, there have been multiple proposals to realize fractional quantum Hall physics on lattices which have several advantages over conventional solid state systems. One of the main goals of studying FQH on lattice is also to explore methods to realize anyons and to successfully braid them. In this direction, conformal ?eld theory (CFT) has been a very useful tool to construct analytical states on lattice that describe FQH phases [4, 5] and even anyons [6] on quite large systems. Parent Hamiltonians for these analytical states have been constructed that are few body but non-local [5]. lattice, the ?nite size issues and effects due to the presence of edges. Hence, braiding anyons ef?ciently on modest lattices with open boundaries is also lacking.

Zielgruppe

This book targets researchers in condensed matter physics and computational physics interested in applying fractional quantum Hall effect models to lattice systems. It explores efficient braiding techniques.

Autoren/Hrsg.

Chopra

Über Autor(innen)

Chopra
Dr. Chopra, for your Advanced Mathematical Modeling course, I propose "Nonlinear Tools: Theory Meets Diverse Problems." This book breaks free from the limitations of linear models and dives into the fascinating world of nonlinear mathematics. We'll bridge the gap between theoretical concepts like chaos theory and practical applications, equipping you with powerful tools to tackle real-world complexities.

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Furthermore, recognizing the growing importance of nonlinear tools in data analysis and AI, the book explores their role in machine learning and control systems, highlighting their problem-solving potential. "Nonlinear Tools" is a valuable resource for researchers, scientists, and engineers encountering nonlinearity, and a captivating introduction for anyone interested in the power of this branch of mathematics to revolutionize how we approach complex problems across diverse disciplines.