Related papers: An introduction to spin systems for mathematicians
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
The objective of this work is twofold. On one hand, it is intended as a short introduction to spin networks and invariants of 3-manifolds. It covers the main areas needed to have a first understanding of the topics involved in the…
Condensed matter physics plays a crucial role in modern scientific research and technological advancements, providing insights into the behavior of materials and their fundamental properties. Understanding complex phenomena and systems in…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods…
The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the…
The Worldline Quantum Field Theory (WQFT) has proven to be an efficient tool for calculating observables in gravitational wave physics. In contrast to other QFT-based techniques in the realm of gravitational wave physics, it makes the…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
Worldline quantum field theory (WQFT) has proven itself a powerful tool for classical two-body scattering calculations in general relativity. In this paper we develop a new worldline action involving bosonic oscillators, which enables the…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…
Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…
Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early…