Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
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DOI：
10.1103/physrevb.84.205108
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发表时间：
2011-07
影响因子：
3.7
通讯作者：
S. Al-Assam;S. Clark;C. Foot;D. Jaksch
中科院分区：
文献类型：
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作者：
S. Al-Assam;S. Clark;C. Foot;D. Jaksch
我们研究了关联积态对描述二维自旋模型基态性质的适用性。我们对多体波函数的分析采用平板或键相关器积状态的形式，并通过使用蒙特卡罗最小化来改变相关器来优化能量。对于Ising模型，我们发现斑块相关器最适合于估计能量，而键相关器更真实地捕捉到了预期的长程关联和系统的临界行为。然而，对于反铁磁性海森堡模型，斑块在描述局域和长程关联方面优于键相关器，因为它们包含的局域参数数量要大得多。这些观察结果对将相关器乘积状态应用于其他更复杂的系统具有定量意义，并提供了重要的启发式见解：特别是有必要仔细地根据所考虑的系统、其相互作用和对称性来选择相关器。
We study the suitability of correlator product states for describing ground-state properties of two-dimensional spin models. Our ansatz for the many-body wave function takes the form of either plaquette or bond correlator product states and the energy is optimized by varying the correlators using Monte Carlo minimization. For the Ising model we find that plaquette correlators are best for estimating the energy while bond correlators capture the expected long-range correlations and critical behavior of the system more faithfully. For the antiferromagnetic Heisenberg model, however, plaquettes outperform bond correlators at describing both local and long-range correlations because of the substantially larger number of local parameters they contain. These observations have quantitative implications for the application of correlator product states to other more complex systems, and give important heuristic insights: in particular the necessity of carefully tailoring the choice of correlators to the system considered, its interactions and symmetries.