# Spectrum of the density matrix of a large block of spins of the XY model in one dimension

Spectrum of the density matrix of a large block of spins of the XY model in one dimension 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Spectrum of the density matrix of a large block of spins of the XY model in one dimension

Quantum Information Processing, Volume 10 (3) – Sep 28, 2010
17 pages

/lp/springer_journal/spectrum-of-the-density-matrix-of-a-large-block-of-spins-of-the-xy-3LfpnLD0cv
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0197-7
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 28, 2010

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