On the validity of SLAC fermions for the 1+1D helical Luttinger liquid

Abstract

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 of the U(1) helical Luttinger liquid and compare our results to bosonization. We argue that non-locality and concomitant singularity at the zone edge has important implications. Large momentum transfers yield spurious features already in the noninteracting case. Upon switching interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering such that a single particle gap opens at the Dirac point. Nonetheless, since non-locality allows for charge fluctuations at any length scale, the ground state remains metallic. Hence, SLAC and bosonization results show marked differences already at intermediate coupling strengths.

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

“…slac fermions have been used to study various models of interacting electrons on a lattice. [24][25][26][27] Their sawtooth dispersion creates lattice artefacts which are not removed by reducing the lattice constant. It would be of interest to explore whether tangent fermions can provide an alternative route without those artefacts.…”

“…It has also been implemented in a condensed matter context. [24][25][26][27] In momentum representation, the Hamiltonian takes the form…”

Dynamical properties of quantum many-body systems with long range interactions

“…Introduction.-Quantum many-body systems with longrange (LR) interactions exhibit different and exotic properties compared with their short-range counterparts, as the LR nature of the interaction differentiates them from many universally accepted long-wavelength and low-energy customs governing the short-range ones over the years. For example, the well-known Hohenberg-Mermin-Wagner theorem [1,2] that forbids spontaneous symmetry-breaking of continuous symmetry at finite temperature in low dimensions can be easily circumvented and LR interactions can generate interesting finite temperature transitions [3][4][5][6][7][8][9] and new critical phenonema [10][11][12][13][14][15]. The bedrock in the research of highly entangled quantum matter -the area law scaling of the entanglement entropy -can also be bypassed in LR systems, and the consequent new scaling behavior points towards new guiding principle of quantum entanglement that awaits to be worked out [8,16].…”