Construction of Hamiltonians by supervised learning of energy and entanglement spectra
Construction of Hamiltonians by supervised learning of energy and entanglement spectra
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DOI：
10.1103/physrevb.97.075114
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发表时间：
2017-05
影响因子：
3.7
通讯作者：
Hiroyuki Fujita;Yuya O. Nakagawa;S. Sugiura;M. Oshikawa
中科院分区：
文献类型：
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作者：
Hiroyuki Fujita;Yuya O. Nakagawa;S. Sugiura;M. Oshikawa
关联多体问题普遍存在于物理的各个领域，如凝聚态物理、核物理和统计物理。然而，由于大量自由度的相互作用，通常不可能从第一原理来处理这些问题。因此，构造一个合适的模型，即有效的哈密顿量，是至关重要的。在这里，我们提出了一个简单的方案，利用机器学习从给定的能量或纠缠谱构造哈密顿量。我们将所提出的方案应用于Hubbard模型的半填充态，并将所得到的有效低能自旋1/2模型与基于高阶微扰理论的几种不一致的解析结果进行了比较。我们还表明，我们的方法也可以用来从量子多体状态的纠缠谱构造其纠缠哈密顿量。我们使用$S=1/2$两腿海森堡阶梯的基态来举例说明这一点。我们观察到由于纠缠起源的不同，模型的两个相(Haldane相和Rung Singlet相)的纠缠哈密顿量存在质的差异。在霍尔丹相中，我们发现纠缠哈密顿量本质上是非定域的，可以通过引入各向异性并将系统转变为大的-$D‘相来恢复定域性。讨论了在强关联系统研究和由实验数据建立模型方面的可能应用。
Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely effective Hamiltonian, is essential. Here, we propose a simple scheme of constructing Hamiltonians from given energy or entanglement spectra with machine learning. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin-1/2 model with several analytic results based on the high order perturbation theory which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the $S=1/2$ two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane phase and the Rung Singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is non-local by nature, and the locality can be restored by introducing the anisotropy and turning the system into the large-$D$ phase. Possible applications to the study of strongly-correlated systems and the model construction from experimental data are discussed.