Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany.
Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa.
Phys Rev Lett. 2018 Dec 14;121(24):240403. doi: 10.1103/PhysRevLett.121.240403.
Slow quenches of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate δ by means of a Holstein-Primakoff expansion about the mean-field value. Unlike in the case of short-range interactions, scaling laws in the LMG model are only found for a ramp starting or ending at the critical point. If instead the ramp is symmetric, as in the typical Kibble-Zurek scenario, then the number of excitations exhibits a crossover behavior as a function of δ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.
在自旋系统的顺磁-铁磁相变过程中，缓慢的磁场猝灭会产生热量。在具有短程相互作用的系统中，热量表现出与猝灭速率呈普适幂律关系的标度，这被称为 Kibble-Zurek 标度。在这项工作中，我们分析了 Lipkin-Meshkov-Glick (LMG) 模型中磁场的缓慢猝灭，该模型描述了完全连接的量子自旋。我们通过在平均场值附近进行 Holstein-Primakoff 展开，解析地确定了量子贡献的剩余热量作为猝灭速率 δ 的函数。与短程相互作用的情况不同，LMG 模型中的标度律仅在斜坡起始或结束于临界点时才成立。如果斜坡是对称的，就像典型的 Kibble-Zurek 情况一样，那么激发数作为 δ 的函数表现出交叉行为，并在热力学极限下趋于常数。先前的、看似矛盾的理论研究被确定为这一动力学的特定极限。我们的结果可以在包括量子气体和囚禁离子在内的几个实验平台上进行测试。
