Comparing quantum fluctuations in the spin-1/2 and spin-1 XXZ Heisenberg models on square and honeycomb lattices
arxiv(2024)
摘要
We present a detailed investigation of the XXZ Heisenberg model for
spin-1/2 and spin-1 systems on square and honeycomb lattices. Utilizing the
density-matrix renormalization group (DMRG) method, complemented by Spiral
Boundary Conditions (SBC) for mapping two-dimensional (2D) clusters onto
one-dimensional (1D) chains, we meticulously explore the evolution of staggered
magnetization and spin gaps across a broad spectrum of easy-axis anisotropies.
Our study reveals that, despite the lower site coordination number of honeycomb
lattice, which intuitively suggests increased quantum fluctuations in its
Néel phase compared to the square lattice, the staggered magnetization in the
honeycomb structure exhibits only a marginal reduction. Furthermore, our
analysis demonstrates that the dependence of staggered magnetization on the XXZ
anisotropy Δ, except in close proximity to Δ=1, aligns with
series expansion predictions up to the 12th order. Notably, for the S=1/2
honeycomb lattice, deviations from the 10th order series expansion predictions
near the isotropic Heisenberg limit emphasize the critical influence of quantum
fluctuations on the spin excitation in its Néel state. Additionally, our
findings are numerically consistent with the singular behavior of the spin gap
near the isotropic Heisenberg limit as forecasted by spin-wave theory. The
successful implementation of SBC marks a methodological advancement,
streamlining the computational complexity involved in analyzing 2D models and
paving the way for more precise determinations of physical properties in
complex lattice systems.
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