Entanglement Spectrum for the XY Model in One Dimension

Abstract

We consider the 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 the expression of the Renyi entropy in terms of modular functions. The eigenvalues λ_n form an exact geometric sequence. For example, for strong magnetic field λ_n = C \exp{(-πτ_0 n)}, here τ_0>0 and C > 0 depend on the anisotropy and the magnetic field. Different eigenvalues are degenerated differently. The largest eigenvalue is unique, but the degeneracy g_n increases sub-exponentially as eigenvalues diminish: g_n \sim \exp{(π\sqrt{n/3})}. For weak magnetic field expressions are similar.

13 pages, 5 figures

References in corpus (5)

• Entanglement spectra of critical and near-critical systems in one dimension
• Entanglement entropy in quantum spin chains with finite range interaction
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Nonequilibrium, thermostats and thermodynamic limit
• The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain

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