1+1 维中 U(1) 对称性破缺的相互作用量子临界性
Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions
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中文总结 AI 辅助
本文在1+1维自旋链中展示了U(1)对称性的自发破缺和相互作用量子临界点，通过子系统Binder标度确定临界指数ν=0.60±0.02和z=1.986±0.005，表明其机制不同于无阻挫模型。
中文摘要 AI 辅助
Hohenberg-Mermin-Wagner 定理促使人们预期一维量子基态中连续对称性保持不破缺。然而，与此预期相反，我们展示了在晶格自旋-1/2 和自旋-1 链中 U(1) 自旋旋转对称性的自发破缺以及相互作用量子临界点的出现。利用子系统 Binder 标度，我们定位了临界点，并确定关联长度临界指数为 ν = 0.60 ± 0.02，这不同于高斯值 0.5，但与微扰重整化群预测一致。我们进一步分析了最低中性激发隙的有限尺寸标度，得到动力学临界指数 z = 1.986 ± 0.005。结果 z < 2 与通过无阻挫模型实现该临界理论的微观机制不相容，暗示了一维量子基态中连续对称性破缺的机制不同于无阻挫性。
英文摘要
The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-$1/2$ and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as $ν= 0.60 \pm 0.02$, distinct from the Gaussian value $0.5$ but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent $z=1.986 \pm 0.005$. The result $z < 2$ is incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.
发表机构
- Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）
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