Density-matrix renormalization-group analysis of quantum critical points: Quantum spin chains

2000/01/31 by Shan-Wen Tsai, J. B. Marston · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.62.5546

published as Phys. Rev. B 62, (2000) 5546 · 21 pages, 12 figures, new results and added references, to appear in PRB

arxiv created 2000/06/06 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a simple method, combining the density-matrix renormalization-group algorithm with finite-size scaling, which permits the study of critical behavior in quantum spin chains. Spin moments and dimerization are induced by boundary conditions at the chain ends and these exhibit power-law decay at critical points. Results are presented for the spin-1/2 Heisenberg antiferromagnet; an analytic calculation shows that logarithmic corrections to scaling can sometimes be avoided. We also examine the spin-1 chain at the critical point separating the Haldane gap and dimerized phases. Exponents for the dimer-dimer and the spin-spin correlation functions are consistent with results obtained from bosonization.

Citations

• Variational and density-matrix renormalization-group studies of the frustrated antiferromagnetic Heisenberg S=1 quantum spin chain
• Density profiles, Casimir amplitudes, and critical exponents in the two-dimensional Potts model: A density-matrix renormalization study
• Density Matrix Renormalization Group Method for 2D Classical Models
• The critical properties of the two-dimensional xy model
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
• Edge magnetic field in thexxzspin- chain

Cited by

• New trends in density matrix renormalization