Strongly correlated chiral fermions on a lattice: Luttinger liquids and symmetric mass generation

Vladimir Zakharov presents the tangent-fermion approach to simulating a single chiral fermion on a lattice. Conventional local discretizations that preserve chirality generate unwanted copies of the Dirac cone. Tangent fermions retain one cone and ordinary on-site chiral symmetry by allowing nonlocal hopping. Other elements remain local: the generalized eigenvalue problem, a Euclidean action suitable for quantum Monte Carlo without a sign problem, and an exact matrix-product operator with fixed bond dimension for tensor-network calculations. Applications illustrate Luttinger-liquid behaviour, spontaneous symmetry breaking at a quantum spin Hall insulator’s edge, and symmetric mass generation in the 3-4-5-0 model.