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

Author： Franchini F.  

Publisher： Springer Publishing Company

ISSN： 1570-0755

Source： Quantum Information Processing, Vol.10, Iss.3, 2011-06, pp. : 325-341

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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.

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