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首页> 外文期刊>Physical review >Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity
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Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

机译：周期性系统中量子临界点的猝灭：缩放定律对周期性的依赖

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摘要

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/τ across a quantum critical point, we find that the density of defects thereby produced scales as 1/τ~(q/(q+1)), deviating from the 1/τ~(1/2) scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of r, although it may exhibit a crossover at intermediate values of r. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.
机译：我们研究具有哈密顿量的具有空间周期性的一维多体系统的淬灭动力学。具体来说，我们考虑具有相同xx和yy偶合且在z方向上受到周期性变化磁场的自旋1/2链，或者等效地，具有周期性局部化学势的无自旋费米子的紧密结合模型，其周期为2q，其中q是一个正整数。对于在整个量子临界点上以1 /τ的速率对磁场强度（或化学势）的强度进行线性淬灭，我们发现由此产生的缺陷密度为1 /τ〜（q /（q + 1） ）），偏离了一系列系统中普遍存在的1 /τ〜（1/2）标度。我们通过将系统的低能量物理性质映射到一组铁电两能级系统来分析这种行为，该系统由经历非线性猝灭的晶格动量k以及执行数值模拟来标记。我们还表明，如果磁场是不同周期的叠加，则幂定律仅取决于r的很大值的最小周期，尽管它可能在r的中间值处表现出交叉。最后，对于自旋链中也存在zz偶合的情况，或等效地，在铁离子系统中存在相互作用的情况，我们认为与定标定律相关的幂取决于q和相互作用强度的组合。

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