Real-space renormalization group approach for the corner Hamiltonian

TL;DR

This paper introduces a real-space renormalization group method for the corner Hamiltonian, connecting it to the density matrix in DMRG, and demonstrates its effectiveness on spin chain models, including integrable and non-integrable cases.

Contribution

It develops a self-consistent RG approach for the corner Hamiltonian and applies it to spin chains, providing insights into the spectrum of non-integrable models.

Findings

Results agree with exact solutions for the XXZ chain.

The method reveals the eigenvalue spectrum characteristics of non-integrable models.

Demonstrates the applicability of the approach to different spin chain systems.

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.