Luttinger liquid behavior in spin chains with a magnetic field

2002/08/31 by Gabor Fath, Gábor Fáth · 2 citations
Physics and Astronomy · #Antiferromagnetism #Chain (unit) #Condensed matter physics #Density matrix renormalization group #Luttinger liquid #Magnetic field #Magnetization #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Renormalization group #Spin (aerodynamics) #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.68.134445

published as Phys. Rev. B 68, 134445 (2003) · Final version, 6 pages, 6 EPS figures

openalex publication_date 2003/10/24 · arxiv created 2003/11/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic field are Luttinger liquids, whose parameters depend on the actual magnetization of the chain. Here we present precise numerical estimates of the Luttinger liquid dressed charge Z, which determines the critical exponents, by calculating the magnetization and quadrupole operator profiles for S=1/2 and S=1 chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.

Citations

• Bosonization and Strongly Correlated Systems
• Haldane-gapped spin chains as Luttinger liquids: Correlation functions at finite field
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
• HEISENBERG INTEGER SPIN CHAINS IN A UNIFORM MAGNETIC FIELD

Cited by

• Magnetic phase diagram of the spin-12antiferromagnetic zigzag ladder
• Phase diagram and continuous pair-unbinding transition of the bilinear-biquadraticS=1Heisenberg chain in a magnetic field