Entanglement entropy of two disjoint blocks in XY chains

By M. Fagotti, Pasquale Calabrese. 2010

165 citations recorded by the source corpus.

We study the Rényi entanglement entropies of two disjoint intervals in XY chains. We exploit the exact solution of the model in terms of free Majorana fermions and we show how to construct the reduced density matrix in the spin variables by taking the Jordan–Wigner string between the two blocks properly into account. From this we can evaluate any Rényi entropy of finite integer order. We study in detail critical XX and Ising chains and we show that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly. We also report results for the gapped phase and after a quantum quench.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/89fcac14bfd30ce36f83d194ab830c990ddf6140

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. M. Fagotti
5. A. Allais
6. F. Essler
7. T. Takayanagi
8. Thomas Hartman

In Condensed Matter Physics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. A. Allais
5. M. Fagotti
6. F. Essler
7. T. Takayanagi
8. T. Nishioka

In Statistical and Nonlinear Physics

1. Pasquale Calabrese
2. E. Tonni
3. J. Cardy
4. M. Fagotti
5. A. Allais
6. F. Essler
7. T. Takayanagi
8. R. Myers

Citations in the corpus

• Entanglement entropy of two disjoint intervals in conformal field theory: II (2010, background): “[17]), or to a finite system at finite temperature.”
• Finite temperature entanglement negativity in conformal field theory (2014, methodology): “Their calculation is a real tour de force which has been performed explicitly only in few instances [42, 43, 44, 45, 46, 47, 48, 49, 50, 51] (exploiting old results of CFT on orbifolds [52, 53, 54, 55]) and agree with some explicit numerical and analytical computations [42, 43, 47, 48, 56, 57, 58, 5”
• Holographic evolution of the mutual information (2011, background): “Detailed studies of I(A1, A2) for spin chain models have also been done [19, 20, 21, 22].”
• Entanglement negativity in extended systems: a field theoretical approach (2012, background): “Some other partial results are also known [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52].”
• Entanglement entropy of two disjoint intervals in conformal field theory (2009, background): “ 2 ;(52) obtained (and checked against numerical calculations) in Ref. [15]. For n = 3;4 numerical estimates of these functions have been obtained from the exact diagonalization of the Ising chain in [17]. The comparison of our prediction with the numerical data for n= 3 and n= 4 is reported in Fig.”
• Quantum quenches in the transverse field Ising chain: II. Stationary state properties (2012, background): “However, in cases where the subsystem A1 consists of several disjoint blocks, the reduced density matrix will not have a simple form like (16) even in the absence of interactions [63].”