Real-space renormalization group approach for the corner Hamiltonian

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.

7 pages

References in corpus (9)

• The density-matrix renormalization group
• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Corner Transfer Matrix Renormalization Group Method
• Density-Matrix Spectra of Solvable Fermionic Systems
• Density-matrix spectra for integrable models
• Universal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit
• Casimir Terms and Shape Instabilities for Two-Dimensional Critical Systems

Cited by in corpus (9)

• New Trends in Density Matrix Renormalization
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Product Wave Function Renormalization Group: construction from the matrix product point of view
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Holographic encoding of universality in corner spectra
• Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime