Yang Mingru, Vanhecke Bram, Schuch Norbert
University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria.
University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.
Phys Rev Lett. 2023 Jul 21;131(3):036505. doi: 10.1103/PhysRevLett.131.036505.
New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. We propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 J-Q Heisenberg chain and a one-dimensional version of the deconfined quantum critical points demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.
如果哈密顿量中的对称性破缺项在重整化群流作用下无关紧要，那么在一个不具备这些对称性的哈密顿量的低能谱中，可能会出现新的或扩大的对称性。我们提出一种基于张量网络的算法，用于从任意量子自旋链的基态中数值提取涌现守恒流的晶格算符近似，而无需事先了解其低能有效场论。我们对自旋 - 1/2 J - Q海森堡链和去禁闭量子临界点的一维版本的研究结果，证明了我们的方法在获取涌现晶格卡茨 - 穆迪生成元方面的能力。它也可以被视为一种找到可积模型的局部运动积分以及临界无隙基态的局部母哈密顿量的方法。
