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arXiv:cond-mat/0507195 · Journal of the Physical Society of Japan

Real-Space Renormalization Group Approach for the Corner Hamiltonian

Kouichi Okunishi

Published Dec 1, 2005• 10 citations
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Abstract

We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized Hamiltonian should satisfy in the thermodynamic limit is also derived from the fixed point of the recursion relation for the corner Hamiltonian. We demonstrate the renormalization group algorithm for the $S=1/2$ XXZ spin chain and show that the results are consistent with the exact solution. We further examine the renormalization group for the S=1 Heisenberg spin chain and then discuss the nature of the eigenvalue spectrum of the corner Hamiltonian for the non-integrable model.

DOI
10.1143/jpsj.74.3186

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In this paper we apply an analytical real-space renormalization group formulation which is based on numerical concepts of the density-matrix renormalization group. Within a rigorous mathematical framework we construct nonperturbative renormalization group transformations for the spin-12\frac{1}{2}21​ XXX\mathrm{XXX}XXX Heisenberg model in the finite-temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behavior in the temperature-dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the antiferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques.
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