Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

@article{Okunishi2007WilsonlikeRR,
  title={Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime},
  author={Kouichi Okunishi},
  journal={Journal of the Physical Society of Japan},
  year={2007},
  volume={76},
  pages={063001}
}
  • K. Okunishi
  • Published 26 February 2007
  • Physics
  • Journal of the Physical Society of Japan
We present a novel real-space renormalization group (RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cutoff parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation. 
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References

SHOWING 1-10 OF 12 REFERENCES

Finite-size corrections in the XXZ model and the Hubbard model with boundary fields

The XXZ model and the Hubbard model with boundary fields are discussed. Using the exact solutions of the present models, the finite-size corrections of the ground-state energy and the low-lying

Density matrix formulation for quantum renormalization groups.

  • White
  • Physics
    Physical review letters
  • 1992
A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a

Real-Space Renormalization Group Approach for the Corner Hamiltonian

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-consist...

The renormalization group: Critical phenomena and the Kondo problem

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in

Finite-size corrections in the XY model with a uniform magnetic field and a boundary field

The one-dimensional XY model with a uniform magnetic field and a boundary field is introduced. The present model is solved analytically at its critical point. Using the present analytical result, the

Density‐matrix spectra for integrable models

The spectra which occur in numerical density‐matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This

Conformal anomaly and surface energy for Potts and Ashkin-Teller quantum chains

Exact equivalences between the critical quantum Potts and Ashkin-Teller chains and a modified XXZ Heisenberg chain have recently been derived by Alcaraz et al (1987). The leading finite-size

Numerical solution of S=1 antiferromagnetic spin chains using a truncated basis expansion.

  • XiangGehring
  • Physics
    Physical review. B, Condensed matter
  • 1993
A truncated basis expansion developed recently by the authors is described in detail. The ground-state and first-excited-state properties of the spin-1 bilinear-biquadratic antiferromagnetic chain

Renormalization-group approach to the Anderson model of dilute magnetic alloys. I. Static properties for the symmetric case

The temperature-dependent impurity susceptibility for the symmetric Anderson model is calculated for all physically relevant values of its parameters $U$ (the Coulomb correlation energy) and