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

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 specic 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 efciently on modest lattices with open boundaries is also lacking.

This book offers a cohesive approach to applying local models and efficient braiding techniques for studying Fractional Quantum Hall physics on lattices. It bridges the gap between theoretical concepts and practical applications.

Autorentext
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. "Nonlinear Tools" delves into core principles, exploring nonlinear dynamics, complex systems, and the numerical methods crucial for solving these problems. We'll also analyze nonlinear differential equations and their applications across various fields. But this book goes beyond theory. We'll embark on a journey to see how these powerful tools are used in physics, chemistry, biology, even economics, finance, and social sciences, showcasing their versatility in modeling intricate systems. 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.