基态与低激发态混合态的共享纯度与并发度作为量子相变指标
Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions
AI总结：
本文比较共享纯度与并发度作为量子相变指标的有效性，发现共享纯度在一维和二维J1-J2海森堡模型及横场伊辛模型中能检测并发度遗漏的相变，并揭示奇偶尺寸系统有限尺寸标度指数发散与边界条件相关。
摘要：
我们研究了共享纯度——一种独立于可分-纠缠范式的量子关联度量——作为量子相变指标的有效性，并将其与并发度（一种二分纠缠度量）进行比较。针对所考虑系统的热态、赝热态等，我们考察了这些序参量。在一维J1-J2海森堡量子自旋模型和一维横场量子伊辛模型中，共享纯度在指示量子相变方面与并发度同样有效。在二维J1-J2海森堡量子自旋模型中，共享纯度指示了模型中存在的两个量子相变，而并发度仅检测到其中一个。此外，我们发现，在由一维J1-J2模型支配的奇数和偶数尺寸系统中，序参量在相变附近的有限尺寸标度指数出现发散，这与先前在奇数和偶数腿梯子上的量子自旋系统中报道的现象类似。这种发散很可能与奇数尺寸系统所需的莫比乌斯带式边界条件有关，而对于偶数尺寸系统，通常的周期性边界条件已足够。
英文摘要：
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.
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