# Oxford Quantum Talks Archive

**Reduced Density Matrix in Spin Models**

*State University of New York at Stony Brook*

Quantum Physics and Logic 2010, May 2010, University of Oxford

We consider reduced density matrix of a large block of consecutive spins in the ground states of a Heisenberg spin chain on an infinite lattice. We derive the spectrum of the density matrix using expression of Renyi entropy in terms of modular functions. The eigenvalues lambda_n form exact geometric sequence. For example, for strong magnetic field lambda_n= C exp(-pi tau_0 n), here tau_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 ~ exp(pi sqrt(n/3)). For weak magnetic field expressions are similar.

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