论文标题
地面和低洼激发态的混合物作为量子相变的指标的共同纯度和同意
Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions
论文作者
论文摘要
我们研究了共享纯度的疗效，这是一种量子相关性的度量，该量子相关性独立于可分离性 - 键入范式，作为量子相变指标，而不是同意，这是双分部分的纠缠措施。研究了所考虑的系统的热状态，伪热状态以及更多的订单参数。在一维$ J_1-J_2 $ HEISENBERG量子旋转模型和一维横向场量子ISING模型的情况下，共享的纯度与指示量子相变的并发一样有效。在二维$ J_1-J_2 $ HEISENBERG量子自旋模型中，共享纯度表示模型中存在的两个量子相变，而同意只检测其中一个。此外，我们发现奇数和均匀尺寸的系统中的订单参数的有限尺寸缩放指数，由一维\（J_1-J_2 \）模型控制的奇数和均匀尺寸的系统，就像先前报道的奇数旋转一样，在奇数和均匀的legged ladders上。差异与奇数系统所需的M {Ö}类似于Bius带状的边界条件有关，而对于均匀尺寸的系统，通常的周期性边界条件就足够了。
We investigate the efficacy of shared purity, a measure of quantum correlation that is independent of the separability-entanglement paradigm, as a quantum phase transition indicator in comparison with concurrence, a bipartite entanglement measure. The order parameters are investigated for thermal states, pseudo-thermal states and more, of the systems considered. In the case of the one-dimensional $J_1-J_2$ Heisenberg quantum spin model and the one-dimensional transverse-field quantum Ising model, shared purity turns out to be as effective as concurrence in indicating quantum phase transitions. In the two-dimensional $J_1-J_2$ Heisenberg quantum spin model, shared purity indicates the two quantum phase transitions present in the model, while concurrence detects only one of them. Moreover, we find diverging finite-size scaling exponents for the order parameters near the transitions in odd- and even-sized systems governed by the one-dimensional \(J_1-J_2\) model, as had previously been reported for quantum spins on odd- and even-legged ladders. It is plausible that the divergence is related to a M{ö}bius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient.
