2008/08/31 by Michele Caraglio, F. Gliozzi, Ferdinando Gliozzi · 4 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Conformal field theory #Conformal map #Density matrix #Entropy (arrow of time) #Geometry #Mathematical analysis #Mathematics #Observable #Physics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum field theory #Quantum many-body systems #Quantum mechanics #Replica #Replica trick #Statistical physics #Symmetry breaking #TRACE (psycholinguistics) #Theoretical physics #Twist #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.1088/1126-6708/2008/11/076
published as JHEP0811:076,2008 · 25 pages, 10 figures v2: section 2.1 improved; matches published version
openalex publication_date 2008/11/25 · arxiv created 2008/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the analyzed subsystem consists of a single interval, they disagree whenever the subsystem is composed of more than one connected part. The reasons of this disagreement are explained.