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Oxford Quantum Talks Archive

Reduced Density Matrix in Spin Models

Vladimir Korepin, 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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