We study the Kibble-Zurek mechanism in the transverse Ising chain coupled to a dissipative boson bath, making use of a new numerical method with the infinite time evolving block decimation combined with the discrete-time path integral. We first show the ground-state phase diagram and confirm that a quantum phase transition takes place in the presence of the system-bath coupling. Then we present the time dependence of the energy expectation value of the spin Hamiltonian and the scaling of the kink density with respect to the time period over which the spin Hamiltonian crosses a quantum phase transition. The energy of spins starts to grow from the energy at the ground state of the full system near a quantum phase transition. The kink density decays as a power law with respect to the time period. These results confirm that the Kibble-Zurek mechanism happens. We discuss the exponent for the decay of the kink density in comparison with a theoretical result with the quantum Monte-Carlo simulation. A comparison to an experimental study is also briefly mentioned.

中文翻译：

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耗散横向Ising链中的Kibble-Zurek机制

我们研究了与耗散玻色子浴耦合的横向 Ising 链中的 Kibble-Zurek 机制，利用无限时间演化块抽取结合离散时间路径积分的新数值方法。我们首先展示了基态相图，并确认在系统-浴耦合存在的情况下发生了量子相变。然后我们展示了自旋哈密顿量的能量期望值的时间依赖性和扭结密度相对于自旋哈密顿量跨越量子相变的时间段的缩放。自旋的能量从接近量子相变的整个系统的基态能量开始增长。扭结密度作为幂律随时间衰减。这些结果证实了 Kibble-Zurek 机制的发生。我们讨论了扭结密度衰减的指数与量子蒙特卡罗模拟的理论结果。还简要提到了与实验研究的比较。