Luttinger liquid and mass generation on a lattice

Résumé :

The helical edge of a quantum spin Hall insulator hosts a one-dimensional metallic state with spin-momentum locking, realizing a helical Luttinger liquid (HLL). While the gapless phase is well understood analytically through bosonization in its simplest form, more complex questions that demand numerical treatment, have remained largely inaccessible to address for a long time. The core obstacle is the fermion-doubling problem: any local and symmetry-preserving discretization of the Hamiltonian on a strictly one-dimensional lattice either introduces spurious low-energy modes or lifts the Dirac point, breaking the topological protection of the cone.
In this talk I describe how this obstruction can be circumvented using a tangent fermion discretization. This preserves time-reversal symmetry and spin-momentum locking at the lattice level, without invoking a two-dimensional bulk. I present the application of this method first to the gapless HLL, where numerical results are in quantitative agreement with bosonization predictions, establishing the framework as a reliable numerical tool. And then I turn to interaction-induced mass generation, including spontaneous time-reversal symmetry breaking in HLL and symmetric mass generation in 3-4-5-0 model, where full analytical treatment is out of reach.

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Contact : serge.florens@neel.cnrs.fr