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International Journal of Modern Physics B

STUDY ON REGULAR DILUTIONS OF $S=\frac{1}{2}$ IMPURITY IN S=1 CHAINS BY QUANTUM MONTE CARLO SIMULATIONS

Huawen Wang, Zhaoxin Xu, He-Ping Ying, Jun Zhang

Published Dec 30, 2003• 1 citation
Publisher

Abstract

We investigate the variant regularly diluted situations of [Formula: see text] in S=1 isotropic antiferromagnetic chains by the quantum Monte Carlo loop cluster algorithm. Our results manifest significant different magnetic properties in the ground state with respect to the odd (even) host S=1 spins in one unit cell with an impurity S=1/2, and the doped system gradually transits to the pure Haldane chain in two different tendencies with the decreasing of the impurity concentrations.

DOI
10.1142/s0217979203023483

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STUDY ON REGULAR DILUTIONS OF S=12S=\frac{1}{2}S=21​ IMPURITY IN S=1 CHAINS BY QUANTUM MONTE CARLO SIMULATIONS
We investigate the variant regularly diluted situations of [Formula: see text] in S=1 isotropic antiferromagnetic chains by the quantum Monte Carlo loop cluster algorithm. Our results manifest significant different magnetic properties in the ground state with respect to the odd (even) host S=1 spins in one unit cell with an impurity S=1/2, and the doped system gradually transits to the pure Haldane chain in two different tendencies with the decreasing of the impurity concentrations.
The effects of regular S=1 dilution of S=1/2 isotropic antiferromagnetic chain are investigated by the quantum Monte Carlo loop/cluster algorithm. Our numerical results show that there are two kinds of ground-state phases which alternate with the variation of S1=1S^1=1S1=1 concentration. When the effective spin of a unit cell is half-integer, the ground state is ferrimagnetic with gapless energy spectrum and the magnetism becomes weaker with decreasing of the S1S^1S1 concentration ρ=1/Mρ= 1/Mρ=1/M. While it is integer, a non-magnetic ground state with gaped spectrum emerges and the gap gradually becomes narrowed as fitted by a relation of Δ≈1.25ρΔ\approx 1.25\sqrtρΔ≈1.25ρ​.
We explore low-lying excited states as well as the ground state of the antiferromagnetic S=1 bond-alternating chain with an S=1/2 impurity spin. For the case where the ground-state phase of the host system is the Haldane phase, we review a numerical analysis of the electron-spin-resonance experimental results on the NENP:Cu2+ system. For the case where the ground-state phase of the host system is the dimer phase, on the other hand, we calculate, using the exact-diagonalization method, the dependences of the energy differences between the ground and low-lying excited states upon both the impurity-host exchange constant and the single-ion-type anisotropy constant, and also calculate, using the density-matrix renormalization-group method, the external-magnetic-field dependence of the impurity-spin magnetizaion in the ground state. In these calculations, we keep the NTENP:Cu2+ system in mind to choose the value of the bond-alternation parameter. We find that a few low-lying excited states which are expected from the valence-bond-solid picture appear as the impurity states in the energy gap between the singlet ground and triplet first-excited states (the dimer gap). Furthermore, for certain values of the above constants, we find that the impurity-spin magnetizaion shows a clear jump at a magnetic field which is in the dimer-gap region or in the magnetization-plateau region of the host system, and also that the impurity-spin magnetizaion has a magnetic-field region where it decreases as a function of the magnetic field.
Using an impurity density-matrix renormalization-group scheme, we establish a reliable picture of how the low-lying energy levels of an S=1S=1S=1 Heisenberg antiferromagnetic chain change quantitatively upon bond doping. An impurity state gradually occurs in the Haldane gap as ${J}^{\ensuremath{'}}<J$, while it appears only if $\frac{{J}^{\ensuremath{'}}}{J}>{\ensuremath{\gamma}}_{c}$ with $\frac{1}{{\ensuremath{\gamma}}_{c}}=0.708$ as ${J}^{\ensuremath{'}}>J$. The spin polarization in the impurity state shows a localization-delocalization transition at ${\ensuremath{\gamma}}_{c}$. The system is nonperturbative as $1<~\frac{{J}^{\ensuremath{'}}}{J}<~{\ensuremath{\gamma}}_{c}$. It can explain the appearance of a new state in the Haldane gap recently observed experimentally on ${\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}\mathrm{BaNi}{\mathrm{O}}_{5}$ [J.F. DiTusa et al., Phys. Rev. Lett. 73, 1857 (1994)].
Low-lying excited states as well as the ground state of the spin-1 antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by means of a method of numerical diagonalization. The isotropic nearest-neighbor exchange coupling plus the uniaxial single-ion-type anisotropy energy is assumed for the host-system Hamiltonian. The energy differences between the ground state and the low-lying excited states, which appear in the Haldane gap, are estimated in the thermodynamic limit. The results are used to analyze the electron-spin-resonance experimental data on Ni(C2_22​H8_88​N2_22​)2_22​NO2_22​(ClO4_44​), abbreviated NENP, containing a small amount of spin-1/2 Cu2+^{2+}2+ impurities. It is found that in this system, the impurity-host (\bigl((Cu2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling is ferromagnetic and its magnitude is about 5 \,\% of the magnitude of the host-host (\bigl((Ni2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling.
Results of a numerical experiment on one-dimensional quantum spin chains are reported. The Heisenberg model with a nearest-neighbor interaction is investigated for spins 1/2\ensuremath{\le}S\ensuremath{\le}2. The procedure of measurement in the conventional checkerboard world-line algorithm is modified to give lower systematic errors. In addition to spatial-correlation properties, the magnon spectral density is extracted from the magnon Green function via the fast maximum-entropy algorithm. In particular, the existence of the Haldane gap in S=1 and S=2 cases is explicitly demonstrated. Hidden antiferromagnetic order peculiar to the Haldane phase is measured for S=1 as a function of one-site anisotropy. The mapping onto the restricted solid-on-solid model is analyzed. The difference between systems with even and odd integer spins is discussed.
Full magnetization curves of S=1 antiferromagnetic Heisenberg chains with periodic and open boundaries are investigated by a quantum Monte Carlo method. The boundary condition has a significant effect on the magnetization process especially in the field range where the Zeeman energy is less than the Haldane gap. The magnetization of the periodic chain in the range is strongly suppressed at low temperatures because the ground state is nonmagnetic. On the other hand, the magnetic ground of the open chain bring about finite magnetization. The difference between both the magnetization curves is also investigated in detail by subtracting the magnetization of the periodic chain with L spins from one of the open chains with L+1 spins. It agrees well with the double of the Brillouin function for S=1/2, rather than the Brillouun function for S=1.