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Coefficients of bosonized dimer operators in spin-1/2 XXZ chains and their applications

机译：自旋1/2 XXZ链中的玻化二聚体算子的系数及其应用

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摘要

Comparing numerically evaluated excitation gaps of dimerized spin-1-2 XXZ chains with the gap formula for the low-energy effective sine-Gordon theory, we determine coefficients d_(xy) and d_z of bosonized dimerization operators in spin-1/2 XXZ chains, which are defined as (-1)~j(S_j~xS_(j+1)~xS_j~yS_(j+1)~y)=d_(Xy) sin[√4πφ(x)]+… and (-1)~jS_j~zS_(j+1)~z=d_z sin[[√4πφ(x)]+…. We also calculate the coefficients of both spin and dimer operators for the spin-1/2 Heisenberg antiferromagnetic chain with a nearest-neighbor coupling J and a next-nearest-neighbor coupling J_2=0.2411J. As applications of these coefficients, we present ground-state phase diagrams of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders with a four-spin interaction. The optical conductivity and electric polarization of one-dimensional Mott insulators with Peierls instability are also evaluated quantitatively.
机译：将数值化评估的自旋1-2 XXZ链的激发间隙与低能有效正弦-戈登理论的间隙公式进行比较，我们确定自旋1/2 XXZ链中的玻化二聚化算子的系数d_（xy）和d_z ，定义为（-1）〜j（S_j〜xS_（j + 1）〜xS_j〜yS_（j + 1）〜y）= d_（Xy）sin [√4πφ（x）] +…和（- 1）〜jS_j〜zS_（j + 1）〜z = d_z sin [[√4πφ（x）] +...。我们还计算了具有最近邻居耦合J和次邻居邻居J_2 = 0.2411J的自旋1/2海森堡反铁磁链的自旋和二聚算子的系数。作为这些系数的应用，我们呈现了磁场中二聚化自旋链的基态相位图和具有四轴相互作用的反铁磁自旋阶梯。还定量评估了具有Peierls不稳定性的一维Mott绝缘子的光导率和电极化。

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