Takahashi Kazutaka
Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062117. doi: 10.1103/PhysRevE.87.062117. Epub 2013 Jun 12.
We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the Schrödinger equation. For several typical systems such as the XY spin chain and the Lipkin-Meshkov-Glick model, the driving Hamiltonian is constructed explicitly. We discuss possible interesting situations when the driving Hamiltonian becomes time independent and when the driving Hamiltonian is equivalent to the original one. For many-body systems, a crucial problem occurs at the quantum phase transition point where the energy gap between the ground and first excited states becomes zero. We discuss how the defect can be circumvented in the present method.
我们将含时量子系统的无跃迁量子驱动方法应用于自旋系统。对于给定的哈密顿量，构造驱动哈密顿量使得原系统的绝热态服从薛定谔方程。对于诸如XY自旋链和Lipkin-Meshkov-Glick模型等几个典型系统，明确构造了驱动哈密顿量。我们讨论了驱动哈密顿量与时间无关以及驱动哈密顿量与原哈密顿量等效时可能出现的有趣情形。对于多体系统，在基态与第一激发态之间的能隙变为零的量子相变点会出现一个关键问题。我们讨论了在当前方法中如何规避该缺陷。
