渐近自由的丧失：二维O(N>2)非线性σ模型中的复杂共形场论及其在海森堡自旋链中的实现
Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains
AI总结：
研究发现二维O(N)非线性σ模型在N>2时渐近自由，存在复耦合平面中的非平凡固定点，通过复共形场论描述，该固定点在非厄米特模型中普遍出现，通过数值验证在自旋链中实现，展示了复中心电荷与标度维数的一致性。
摘要：
二维O(N)非线性σ模型（NLSM）在N>2时渐近自由：它既没有非平凡固定点也无自发对称破缺。本文表明在复耦合平面中普遍存在非平凡固定点，由复共形场论（CCFT）描述。该CCFT固定点具有单一相关单极子算符，因此预期出现在任何具有O(N)对称性的非厄米特模型中，通过调节单一复参数。我们通过在两个非厄米特自旋-1反铁磁海森堡链和一个非厄米特自旋-1/2阶梯中定位CCFT于N=3，证实了复中心电荷和标度维数与通过实固定点分析延续得到的结果一致。我们进一步构建了一个自旋-1链的现实利德布兰德算子，其无点击动力学由非厄米特哈密顿量实现CCFT。由于CCFT真空是衰减率最小的本征态，系统在耗散动力学下自然弛豫至CFT状态，从而提供了一条通过工程耗散制备长程纠缠态的途径。
英文摘要：
The two-dimensional $O(N)$ nonlinear sigma model (NLSM) is asymptotically free for $N>2$: it exhibits neither a nontrivial fixed point nor spontaneous symmetry-breaking. Here we show that a nontrivial fixed point generically does exist in the complex coupling plane and is described by a complex conformal field theory (CCFT). This CCFT fixed point is generic in the sense that it has a single relevant singlet operator, and is thus expected to arise in any non-Hermitian model with $O(N)$ symmetry upon tuning a single complex parameter. We confirm this prediction numerically by locating the CCFT at $N = 3$ in two non-Hermitian spin-1 antiferromagnetic Heisenberg chains, and in a non-Hermitian spin-$1/2$ ladder, finding good agreement between the complex central charge and scaling dimensions and those obtained by analytic continuation of real fixed points from $N\leq 2$. We further construct a realistic Lindbladian for a spin-1 chain whose no-click dynamics are governed by the non-Hermitian Hamiltonian realizing the CCFT. Since the CCFT vacuum is the eigenstate with the smallest decay rate, the system naturally relaxes under dissipative dynamics toward a CFT state, thus providing a route to preparing long-range entangled states through engineered dissipation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
