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arXiv:cond-mat/0011320 · Physical review. B, Condensed matter

Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field

Takashi Hikihara, Akira Furusaki

Published Mar 15, 2001• 71 citations
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Abstract

We study the ground-state spin correlations in the gapless incommensurate regime of a $S=1/2$ $\mathrm{XXZ}$ chain and a two-leg antiferromagnetic ladder under a magnetic field, in which the gapless excitations form a Tomonaga-Luttinger (TL) liquid. We calculate numerically the two-spin correlation functions and the local magnetization in the two models using the density-matrix renormalization-group method. By fitting the numerical results for an open $\mathrm{XXZ}$ chain of 100 spins to correlation functions of a Gaussian model, we determine the TL-liquid parameter K and the amplitudes of the correlation functions. The value of K estimated from the fits is in excellent agreement with the exact value obtained from the Bethe ansatz. We apply the same method to the open ladder consisting of 200 spins and determine the dependence of K on the magnetization M. The $K\ensuremath{-}M$ relation changes drastically depending on the ratio of the coupling constants in the leg and rung directions. We also discuss implications of these results to experiments on the nuclear spin relaxation rate ${1/T}_{1}$ and dynamical spin structure factors.

DOI
10.1103/physrevb.63.134438

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We study the one-dimensional spin-12\frac{1}{2}21​ Heisenberg model with antiferromagnetic nearest-neighbor J1{J}_{1}J1​ and next-nearest-neighbor J2{J}_{2}J2​ exchange couplings in magnetic field hhh. With varying dimensionless parameters J2/J1{J}_{2}/{J}_{1}J2​/J1​ and h/J1h/{J}_{1}h/J1​, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave (SDW2)({\text{SDW}}_{2})(SDW2​), and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW2{\text{SDW}}_{2}SDW2​, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge c=1+1c=1+1c=1+1), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.
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