# 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} }

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

- Physics
- 1996

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.

- PhysicsPhysical 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

- Physics
- 2005

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

- Physics
- 1975

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

- Physics
- 1995

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

- Physics
- 1999

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

- Physics
- 1987

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.

- PhysicsPhysical 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

- Physics
- 1980

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…