# Probability and Mathematical Physics Seminar

#### Entanglement entropy in quantum spin chain models

**Speaker:**
Jani Virtanen, University of Reading

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, February 14, 2020, 11:10 a.m.

**Synopsis:**

I discuss entanglement entropy of bipartite systems using the von Neumann entropy as measure of entanglement. Some of the most widely studied systems include one-dimensional quantum critical systems, such as quantum spin chains, which in their simplest setting consist of $N$ spins. Of particular interest is the XX spin chain model with zero magnetic field and the study of the von Neumann entropy of the subsystem $P$ of spins on lattice sites $\{1,2,\dots,m\}\cup\{2m+1,2m+2,\dots, 3m\}$, which can be analyzed using certain integral representations. For a single block subsystem, the integral representation involves Toeplitz determinants and the entropy can be calculated using the Fisher-Hartwig asymptotic expansion of these determinants. In this talk, we consider a subsystem that consists of two blocks of spins separated by one spin and compute the mutual information between the two intervals explicitly and rigorously using the Riemann-Hilbert approach. Joint work with György Gehér (Reading University) and Alexander Its (Indiana University-Purdue University Indianapolis).