Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany.
Phys Rev Lett. 2013 Jun 28;110(26):260403. doi: 10.1103/PhysRevLett.110.260403. Epub 2013 Jun 26.
We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two-dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to the "tower of states" Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. We briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.
我们研究了二维正方形晶格上单位填充的玻色-哈伯德模型的纠缠能谱（ES），包括莫特绝缘相和超流相。在莫特相中，我们证明 ES 主要由两个子系统之间边界处的物理现象所决定。在边界局域（微扰）结构之上，ES 还表现出源自边界上一维色散的子结构。在超流相中，ES 的结构在性质上有所不同，反映了该相的自发破缺 U(1) 对称性。我们将基本的低能结构归因于模型的“态塔”哈密顿量。然后，我们讨论了这些特征结构如何在超流到莫特绝缘相变中演变，以及它们对纠缠熵行为的影响。我们简要概述了 ES 结构对二维矩阵乘积态算法效率的影响。
