Localization for Random Block Operators Related to the XY Spin Chain

Dynamic Correlations in a Random Spin-1/2 XY Chain

We examine dynamic quantities of a random spin-1/2 isotropic XY chain in a transverse field. The randomness is related to the sign of the nearest-neighbor exchange interaction and can be eliminated by a suitable transformation. As a result, the dynamic quantities for the random spin chain are related to the same dynamic quantities for the homogeneous spin chain. We use the available results for...

A solvable model of a random spin-12 XY chain

The paper presents exact calculations of thermodynamic quantities for the spin2 isotropic XY chain with random lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions. PACS codes: 75.10.-b

Introduction to the Mathematics of the XY -Spin Chain

In the following we present an introduction to the mathematical theory of the XY spin chain. The importance of this model lies in the fact, first understood by Lieb, Schultz and Mattis in [4], that the XY spin chain is one of very few “exactly solvable” models in the theory of quantum many-body systems. Lieb, Schultz and Mattis considered the constant coefficient case. In the variable coefficie...

Localization for Random Unitary Operators

We consider unitary analogs of 1−dimensional Anderson models on l2(Z) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of Uω is pure point almost surely for all val...

The Quasi-crystalline Quantum Spin-1⁄2 Xy-chain