Related papers: An introduction to spin systems for mathematicians
Topologically ordered quantum spin systems have become an area of great interest, as they may provide a fault-tolerant means of quantum computation. One of the simplest examples of such a spin system is Kitaev's toric code. Naaijkens made…
We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that…
We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties…
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation…
In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the…
These two lectures give a pedagogical introduction to the ``string-inspired'' worldline technique for perturbative calculations in quantum field theory. This includes an overview over the present range of its applications. Several examples…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
Contents: 1 Frustrated quantum spin systems 1.1 The Pyrochlore checkerboard 1.2 Singlets in reflection symmetric spin systems 2 Wehrl entropy of Bloch coherent states 2.1 Conjectures of Wehrl and Lieb 2.2 Proof of Lieb's conjecture for low…
Entanglement of the ground states in $XXZ$ and dimerized Heisenberg spin chains as well as in a two-leg spin ladder is analyzed by using the spin-spin concurrence and the entanglement entropy between a selected sublattice of spins and the…
In the recent article Phys.\ Lett.\ B {\bf 759} (2016) 424 a new class of field theories called Nonlinear Field Space Theory has been proposed. In this approach, the standard field theories are considered as linear approximations to some…
This is a draft version of Part I of a three-part textbook on quantum field theory.
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
Spin-1 particles, is a fundamental bound state for the two quarks, and play a crucial role in elucidating the electromagnetic properties within the realm of hadronic physics. Their intrinsic relativistic nature mandates a quantum field…