Renyi entropy of the XY spin chain

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...

Renyi Entropy Estimation Revisited

We revisit the problem of estimating entropy of discrete distributions from independent samples, studied recently by Acharya, Orlitsky, Suresh and Tyagi (SODA 2015), improving their upper and lower bounds on the necessary sample size n. For estimating Renyi entropy of order α, up to constant accuracy and error probability, we show the following Upper bounds n = O(1) · 2(1− 1 α )Hα for integer α...

Shannon Entropy , Renyi Entropy , and Information

This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

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

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