Dóra Balázs, Lundgren Rex, Selover Mark, Pollmann Frank
Department of Theoretical Physics and BME-MTA Exotic Quantum Phases Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
Phys Rev Lett. 2016 Jul 1;117(1):010603. doi: 10.1103/PhysRevLett.117.010603. Epub 2016 Jun 29.
Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e., the overlap of the disentangled and final wave functions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wave function. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.
卢廷格液体（LLs）是通过一维相互作用耦合左右移动的粒子而产生的。利用解析和数值方法，通过量子猝灭后的动量空间纠缠来研究LLs这种最自然的划分。我们表明，LL的动量空间纠缠谱在平衡态和量子猝灭后都具有许多普遍特征。最大的纠缠本征值与洛施密特回波相同，即系统解纠缠态和最终波函数的重叠。第二大的本征值是解纠缠系统总动量为零的第一激发态与最终波函数的重叠。纠缠间隙在平衡态和量子猝灭后都是普遍的。动量空间纠缠熵总是广延的，并且在猝灭后迅速饱和到一个与时间无关的值，这与空间二分法形成鲜明对比。
