caa a22 4500 445886544 CHVBK 20180317145601.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s11128-010-0197-7 doi (NATIONALLICENCE)springer-10.1007/s11128-010-0197-7 Spectrum of the density matrix of a large block of spins of the XY model in one dimension [Elektronische Daten] [F. Franchini, A. Its, V. Korepin, L. Takhtajan] We consider reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using expression of Rényi entropy in terms of modular functions. The eigenvalues λ n form exact geometric sequence. For example, for strong magnetic field λ n = C exp(−π τ 0 n), here τ 0>0 and C > 0 depend on anisotropy and magnetic field. Different eigenvalues are degenerated differently. The largest eigenvalue is unique, but degeneracy g n increases sub-exponentially as eigenvalues diminish: $${g_{n}\sim \exp{(\pi \sqrt{n/3})}}$$. For weak magnetic field expressions are similar. Springer Science+Business Media, LLC, 2010 Entanglement nationallicence Entropy nationallicence Entanglement spectrum nationallicence Reduced density matrix nationallicence XY model nationallicence Partitions theory nationallicence Franchini F. The Abdus Salam ICTP, Strada Costiera 11, 34014, Trieste, TS, Italy aut Its A. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 46202-3216, Indianapolis, IN, USA aut Korepin V. C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, 11794-3840, Stony Brook, NY, USA aut Takhtajan L. Mathematics Department, State University of New York at Stony Brook, 11794-3840, Stony Brook, NY, USA aut Quantum Information Processing Springer US; http://www.springer-ny.com 10/3(2011-06-01), 325-341 1570-0755 10:3<325 2011 10 11128 https://doi.org/10.1007/s11128-010-0197-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11128-010-0197-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Franchini F. The Abdus Salam ICTP, Strada Costiera 11, 34014, Trieste, TS, Italy aut NATIONALLICENCE 700 1- Its A. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 46202-3216, Indianapolis, IN, USA aut NATIONALLICENCE 700 1- Korepin V. C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, 11794-3840, Stony Brook, NY, USA aut NATIONALLICENCE 700 1- Takhtajan L. Mathematics Department, State University of New York at Stony Brook, 11794-3840, Stony Brook, NY, USA aut NATIONALLICENCE 773 0- Quantum Information Processing Springer US; http://www.springer-ny.com 10/3(2011-06-01), 325-341 1570-0755 10:3<325 2011 10 11128 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer