Related papers: A new class of completely integrable quantum spin …
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensional, positively graded thin algebras. This paper completes…
We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found…
In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum…
The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical…
The manner in which spin-polarized electrons interact with a magnetized thin film is currently described by a semi-classical approach. This in turn provides our present understanding of the spin transfer, or spin torque phenomenon. However,…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the…
Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n)…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…
The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the…
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…
In this note we present a new self-contained approach to the class field theory of arithmetic schemes in the sense of Wiesend. Along the way we prove new results on space filling curves on arithmetic schemes and on the class field theory of…
We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which…