Related papers: Quantum spin systems on infinite lattices

These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.

This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…

These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and…

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…

We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…

I present an introduction to the field of Quantum Chromodynamics (QCD) with emphasis on nucleon spin structure and perturbative methods. After a somewhat comprehensive overview of perturbative QCD, including the systematics of…

These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…

These pedagogical lecture notes present a general introduction to most aspects of the integer and fractional quantum Hall effects. This is followed by an extensive discussion of quantum Hall ferromagnetism, both for spins in single-layer…

Some recent developments in the theory of quantum spin systems are reviewed.

The growth in the demand for precisely crafted many-body systems of spin-$1/2$ particles/qubits is due to their top-notch versatility in application-oriented quantum-enhanced protocols and the fundamental tests of quantum theory. Here we…

The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization…

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…

These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at https://www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the…

This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…

In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum…

We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…