Defect production due to quenching through a multicritical point and along a gapless line

通过多临界点淬火产生的缺陷

Defect production due to quenching through a multicritical point

通过改变哈密顿量中的一个参数$t/τ$，研究了量子自旋系统在多临界点猝灭时缺陷的产生，其中$τ$是猝灭的特征时间尺度.我们认为，当量子系统在多临界点处猝灭时，最终态的缺陷密度（$n$）不一定由Kibble-Zurek标度形式$n \sim 1/τ^{d ν/(z ν+1)}$给出，其中$d$是空间维数，$ν$和$z$分别是与量子临界点相关的关联长度和动力学指数.我们提出了一个广义的缺陷密度的缩放形式由$n \sim 1/τ^{d/(2z_2)}$，其中的指数$z_2$决定的行为的非对角项的$2 \times 2$朗道-齐纳矩阵在多临界点。这种标度不仅在多临界点处有效，而且在普通临界点处也有效。

量子行走中无能隙相之间的拓扑转变

Topological transition between gapless phases in quantum walks

本文提出利用三步离散时间量子行走模拟费米子链中无能隙相之间的拓扑转变，通过曲率函数标度理论、重正化群流及绕数等方法验证了多临界点处的转变特征。

沿无间隙线淬火：缺陷密度的不同指数

Quenching along a gapless line: A different exponent for defect density

我们使用一个新的淬火计划，研究的一维各向异性$XY$自旋1/2链中存在的横向场之间交替的值$h+\de$和$h-\de$从网站到网站的动力学。在该猝灭方案中，表示相互作用的各向异性的参数（$\ga$）从$-\infty$线性猝灭为$ +\infty$，作为$\ga = t/τ$，保持相互作用的总强度$J$固定。当$\ga$沿着由$h$、$\de$和$\ga$跨越的参数空间中的临界表面$h^2 = \de^2 + J^2$淬火时，系统穿过无间隙相。通过映射到一个等效的两级朗道-齐纳问题，我们表明，在最终状态的缺陷密度尺度为$1/τ^{1/3}$，在以前的研究中没有观察到的行为淬火通过一个无隙相。我们还推广的模型，将额外的交替的各向异性或相互作用的强度，并得出一个相同的结果下类似的淬火。基于上述结果，我们提出了一个一般的缩放的缺陷密度与淬火率$τ$淬火沿无间隙的临界线。

Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e., the exponent varies continuously with the parameter $α$ that defines the path, up to a critical value $α= α_c$; on the other hand for $α\geq α_c$, the scaling exponent saturates to a constant value. We show that dynamically generated and {\it path($α$)-dependent} effective critical exponents associated with th…

Adiabatic dynamics in passage across quantum critical lines and gapless phases

It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system.…

Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders

Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic Néel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends …