论文标题
对具有相对论连续矩阵产品状态的量子SINH-GORDON模型的研究
A study of the quantum Sinh-Gordon model with relativistic continuous matrix product states
论文作者
论文摘要
我使用最近引入的变异方法（相对论连续矩阵乘积状态（RCMP））研究正弦 - 戈登（SG）和Sinh-Gordon（SHG）量子场理论。主要优点是直接在热力学极限下工作，而无需任何紫外线调节剂。 SG模型是充分理解且可以集成的，这为变异方法提供了方便的基准，并作为热身。 RCMP近似于SG模型任意良好的SG模型的基态，直到在等式量化约定中或在CFT约定中$ B = 1/\ sqrt {2} $中的自由费点[耦合$β= \ sqrt {4π} $在CFT约定中] SHG模型虽然可以集成，但知之甚少，其强大的耦合方案$β\约1 $受到争议。 RCMP还将SHG模型的基态拟合到大约$ b = 1/\ sqrt {2} $，之后它们的预测开始显着偏离“确切”结果。这更令人困惑，因为那时SHG模型的物理不会发生任何事情（例如，地面能量密度不会差异）。要么“精确” SHG结果并非精确（SG Bethe bethe Ansatz解决方案的分析延续是不必要的），要么更有可能以SHG接地状态的物理结构的变化，以使其无法达到RCMPS的合理键尺寸范围。
I study the Sine-Gordon (SG) and Sinh-Gordon (ShG) quantum field theories with a recently introduced variational method, the relativistic continuous matrix product states (RCMPS). The main advantage is to work directly in the thermodynamic limit, and without any UV regulator. The SG model is well understood and integrable, which provides a convenient benchmark for the variational method and serves as a warm-up. RCMPS approximate the ground state of the SG model arbitrary well up to the free Fermion point [coupling $β=\sqrt{4π}$ in equal-time quantization convention, or $b=1/\sqrt{2}$ in CFT convention], where the ground energy collapses to $-\infty$, and some renormalized ansatz would be needed. The ShG model, while integrable, is less understood and its strong coupling regime $β\approx 1$ is subject to some controversy. RCMPS also fit the ground state of the ShG model up to approximately $b=1/\sqrt{2}$, after which their predictions start to deviate substantially from the "exact" results. This is more puzzling as nothing is expected to happen physically for the ShG model at that point (eg, the ground energy density does not diverge). Either the "exact" ShG results are not exact (the analytic continuation of the SG Bethe Ansatz solution is unwarranted), or, more likely, the physical structure of the ShG ground state changes in such a way that it becomes out of reach of the RCMPS manifold for reasonable bond dimensions.
