Zakharov V A, Tworzydło J, Beenakker C W J, Pacholski M J
Instituut-Lorentz, <a href="https://ror.org/027bh9e22">Universiteit Leiden</a>, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Faculty of Physics, <a href="https://ror.org/039bjqg32">University of Warsaw</a>, ulica Pasteura 5, 02-093 Warszawa, Poland.
Phys Rev Lett. 2024 Sep 13;133(11):116501. doi: 10.1103/PhysRevLett.133.116501.
The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results because of the fermion-doubling obstruction: a local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here, we show how to work around this obstruction by discretizing both space and time to obtain a local Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum Monte Carlo simulations that preserve the topological protection of an unpaired Dirac cone.
卢廷格模型是一维无质量狄拉克费米子费米液体描述因相互作用而失效的一个范例。在一维晶格上对该模型进行离散化的尝试未能重现已有的玻色化结果，原因是费米子倍增阻碍：哈密顿量的局部且保对称离散化引入了一种虚假的低能激发的第二种粒子，而非局部离散化在狄拉克点处打开了一个单粒子能隙。在此，我们展示了如何通过对空间和时间进行离散化来绕过这一阻碍，从而获得具有哈伯德相互作用的螺旋卢廷格液体的局部拉格朗日量。该方法使得量子蒙特卡罗模拟能够保留未配对狄拉克锥的拓扑保护。
