# Dresden 2014 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 36: Focus Session: Advanced Algorithms for Strongly Correlated Quantum Matter

### TT 36.3: Hauptvortrag

### Dienstag, 1. April 2014, 10:30–11:00, HSZ 03

**Characterizing Entanglement Entropy with Quantum Monte Carlo** — •Roger Melko — University of Waterloo 200 University Ave. W. Waterloo, ON N2L 3G1

An understanding of entanglement across a bipartition can give novel perspectives on correlations in condensed matter systems. Entanglement probes geometric and topological properties of the bipartition, and resultant paradigms such as the ``area'' law have led to important resources for characterizing quantum phases and phase transitions. The full power of these resources has only recently been exploited in two dimensions and higher, since the advent of algorithms to calculation the Renyi entanglement entropies in quantum Monte Carlo (QMC). Estimators for the Renyi entropies, mostly based on replica-trick methods borrowed from quantum field theory, are now routinely exploited in almost all flavours of QMC, including Stochastic Series Expansion, T=0 Projector, Auxiliary Field, and Path Integral Monte Carlo for particles in the continuum. In this talk, I will discuss the common underpinning of all replica-trick methods, as well as some advanced algorithmic tactics required to obtain statistical control of the Renyi entropy estimators. Finally, I will illustrate the use of Renyi entropies as a resource in condensed matter systems, e.g. measurement of topological entanglement entropy in spin liquid phases, identification of broken continuous symmetries, and calculation of universal quantities at quantum critical points.