Sine-Gordon模型与玻色张量网络：连续统匹配与孤子散射
Sine-Gordon Model with Bosonic Tensor Networks: Continuum Matching and Soliton Scattering
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中文总结 AI 辅助
利用玻色张量网络将格点Sine-Gordon模型定量映射到连续统理论，精确匹配耦合参数，无调参恢复孤子质量、色散与呼吸子谱，并模拟孤子碰撞提取Wigner位移，验证连续统预言。
中文摘要 AI 辅助
我们使用玻色张量网络将哈密顿表述下的格点Sine-Gordon模型定量地连接到其连续统理论。通过将格点顶点算符匹配到自由玻色子紫外不动点处的共形归一化，我们得到了裸格点耦合与重整化连续统质量参数之间的精确关系。在整个研究的参数范围内，孤子质量无需可调参数即可逼近Zamolodchikov的精确连续统预测。利用均匀矩阵乘积态和准粒子拟设，我们还在百分之一精度内恢复了相对论性孤子色散关系以及两个最轻的呼吸子质量。我们模拟了高斯孤子-反孤子波包在无反射点附近的实时碰撞，并提取了Wigner空间位移。我们将此位移与从透射相位的动量导数获得的精确连续统预测进行比较，恢复了其特征性的快度依赖性。我们的玻色子模拟为非可积扩展提供了基础，为其他哈密顿格点场论（包括规范理论）中的重整化提供了经验，并为连续变量量子模拟提供了基准。
英文摘要
We use bosonic tensor networks to connect the lattice sine-Gordon model in the Hamiltonian formulation quantitatively to its continuum theory. Matching the lattice vertex operator to its conformal normalization at the free-boson ultraviolet fixed point yields the exact relation between the bare lattice coupling and the renormalized continuum mass parameter. The soliton mass then approaches Zamolodchikov's exact continuum prediction throughout the studied parameter range, without adjustable parameters. Using uniform matrix product states and a quasiparticle ansatz, we also recover the relativistic soliton dispersion and the two lightest breather masses at the percent level. We simulate real-time collisions of Gaussian soliton-antisoliton wave packets near a reflectionless point and extract the Wigner spatial displacement. We compare this displacement with the exact continuum prediction obtained from the momentum derivative of the transmission phase, recovering its characteristic rapidity dependence. Our bosonic simulations provide a foundation for nonintegrable extensions, offer lessons for renormalization in other Hamiltonian lattice field theories, including gauge theories, and provide benchmarks for continuous-variable quantum simulations.
发表机构
- Stony Brook University（石溪大学）
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