约化态稳定器Rényi熵作为阻挫J₁-J₂自旋模型量子相变的探针
Reduced State Stabilizer Rényi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models
中文总结 AI 辅助
本研究提出约化态纯度修正稳定器Rényi熵可作为阻挫J₁-J₂自旋模型量子相变的可靠局域探针，在一维、二维模型的基态及低温亚基态中均展现出优于传统两量子比特纠缠的相变检测能力。
中文摘要 AI 辅助
我们研究了约化两量子比特密度矩阵的二阶纯度修正稳定器Rényi熵（SRE）能否作为阻挫量子自旋系统中量子相变（QPT）的可靠局域指标。我们考虑了一维各向同性J₁-J₂海森堡模型、一维XXZ J₁-J₂模型，以及二维4×4方格晶格上的J₁-J₂海森堡模型。与此前研究的几种无法检测这些阻挫系统基态量子相变的量子信息度量不同，约化基态纯度修正SRE成功识别了大部分相变。对于剩余情况，我们考虑了一个低温亚基态，其建模为基态与第一激发态的统计混合，服从麦克斯韦-玻尔兹曼型占据概率。对于一维各向同性模型，亚基态SRE在临界点处呈现不连续性，得到α_c(∞)=0.24116，与已确立的数值高度吻合；基态SRE则呈现拐点，得到α_c(∞)=0.2681。对于一维XXZ模型，亚基态SRE再现了完整的各向异性依赖相图，而基态SRE仅在低各向异性下捕捉到相变。对于二维模型，亚基态SRE检测到两个相变，对应的α_c(4×4)=0.40781和0.6208，而基态SRE在0.6230处识别出第二个相变。与传统两量子比特纠缠相比，纯度修正SRE在揭示原本不可见的相变方面展现出明显优势，确立了其作为阻挫量子临界性的稳健、高效、局域探针的地位。
英文摘要
We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic \(J_1-J_2\) Heisenberg model, the one-dimensional XXZ \(J_1-J_2\) model, and the two-dimensional \(J_1-J_2\) Heisenberg model on a \(4\times4\) square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding \(α_c(\infty)=0.24116\), in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding \(α_c(\infty)=0.2681\). For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at \(α_c(4\times4)=0.40781\) and \(0.6208\), while the ground-state SRE identifies the second at \(0.6230\). Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.
