National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA.
Phys Rev Lett. 2013 Nov 22;111(21):210402. doi: 10.1103/PhysRevLett.111.210402. Epub 2013 Nov 19.
We show the violation of the entanglement area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on an N(d) Cartesian lattice in d dimensions, e.g., the exciton Bose liquid in two dimensions, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N(d-1)/3)lnL. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary, we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.
我们展示了玻色子系统中玻色表面的纠缠面积定律的违反。对于在 d 维 N(d)笛卡尔格上具有无间隙因子化能量色散的玻色子系统，例如二维激子玻色液体，我们明确地表明，宽度为 L 的带子子系统保持沿 d-1 个笛卡尔轴的平移对称性，具有主导的纠缠熵 (N(d-1)/3)lnL。利用这个结果、强次加性不等式和晶格对称性，我们从下到上限制了矩形子系统的纠缠熵，表明对面积定律的对数违反。对于具有单个平坦边界的子系统，我们也从下到上限制了纠缠熵，表明对数违反，并认为具有任意平滑边界的子系统的纠缠熵也受到类似的限制。
