论文标题
引导量子旋转系统中的间隙
Bootstrapping the gap in quantum spin systems
论文作者
论文摘要
在这项工作中，我们报告了一种新的引导方法，该方法用于量子机械问题，该方法紧密反映了共形场理论（CFT）的设置。我们使用运动方程来开发用于基质元素的保形块膨胀的类似物，并施加交叉对称性，以便在其值上限制界限。该方法可以应用于使用局部哈密顿量的任何量子机械系统，我们可以在Anharmonic振荡器模型以及（1+1）维横向横向场ISING模型（TFIM）上进行测试。对于Anharmonic振荡器模型，我们表明，少数交叉方程为光谱和基质元素提供了准确的解决方案。对于TFIM，我们表明，汉密尔顿运动方程，翻译不变性和全球对称选择规则在热力学极限内对TFIM的间隙和矩阵元素施加了严格的束缚。当我们考虑更大的跨方程系统时，界限会改善，排除更多有限体积的解决方案。我们的方法提供了一种方法，可以严格且无近似值探测来自哈密顿量的无限晶格的低能谱。
In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for matrix elements and impose crossing symmetry in order to place bounds on their values. The method can be applied to any quantum mechanical system with a local Hamiltonian, and we test it on an anharmonic oscillator model as well as the (1+1)-dimensional transverse field Ising model (TFIM). For the anharmonic oscillator model we show that a small number of crossing equations provides an accurate solution to the spectrum and matrix elements. For the TFIM we show that the Hamiltonian equations of motion, translational invariance and global symmetry selection rules imposes a rigorous bound on the gap and the matrix elements of TFIM in the thermodynamic limit. The bound improves as we consider larger systems of crossing equations, ruling out more finite-volume solutions. Our method provides a way to probe the low energy spectrum of an infinite lattice from the Hamiltonian rigorously and without approximation.
