论文标题
（1 + 1） - 维螺旋液体液体的SLAC费米子的有效性
Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid
论文作者
论文摘要
Nielson-Ninomiya定理指出，局部，翻译不变的杂质的自由fermion晶格动作，真正的翻译不变，而真正的fermion则加倍。 SLAC的方法放弃了区域和远程跳跃，导致区域边界上具有奇异性的线性分散体。我们引入了SLAC HAMILTON配方，预计将在幼稚的连续体限制下实现U（1）螺旋Luttinger液体。我们认为，区域边缘的非本地性和伴随奇异性具有重要的含义。在非相互作用的情况下，大动量转移会产生虚假特征。开启相互作用后，非局部性使Mermin-Wagner定理无效，并允许长期磁性排序。实际上，在强耦合中，型号将型号映射到具有$ 1/r^2 $交换的XXZ-Spin链上。在这里，Spin-Wave和DMRG计算都支持长期范围的顺序。虽然长期订单打开了单个粒子间隙的狄拉克点，但区域结合的奇异性仍然存在着相互作用强度的任何有限值，以使基态保持金属。因此，Slac Hamiltonian不会流到$ 1 $ d的螺旋Luttinger液体固定点。除了DMRG模拟外，我们还使用了辅助场量子卡洛模拟来得出上述结论。
The Nielson-Ninomiya theorem states that a chirally invariant free fermion lattice action, which is local, translation invariant, and real necessarily has fermion doubling. The SLAC approach gives up on locality and long range hopping leads to a linear dispersion with singularity at the zone boundary. We introduce a SLAC Hamiltonian formulation that is expected to realize a U(1) helical Luttinger liquid in a naive continuum limit. We argue that non-locality and concomitant singularity at the zone edge has important implications. Large momentum transfers yield spurious features already in the non-interacting case. Upon switching on interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering. In fact, in the strong coupling limit the model maps onto an XXZ-spin chain with $1/r^2$ exchange. Here, both spin-wave and DMRG calculations support long ranged order. While the long-ranged order opens a single particle gap the Dirac point, the singularity at the zone-boundary persists for any finite value of the interaction strength such that the ground state remains metallic. Hence, SLAC Hamiltonian does not flow to the $1$d helical Luttinger liquid fixed point. Aside from DMRG simulations, we have used auxiliary field quantum Monte Carlo simulations to arrive to the above conclusions.
