New Criticality of 1D Fermions

TL;DR

This paper investigates the critical behavior of one-dimensional massive fermions with multi-particle interactions, revealing new universality classes and phase transitions relevant to various physical systems.

Contribution

It introduces exact renormalization group analysis of 1D fermions with multi-body forces, uncovering critical instabilities and new universality classes.

Findings

Finite m-body forces induce a critical transition to fermionic bound states.

Repulsive pair forces lead to free fermion scaling.

New universality classes are identified for interacting fermions.

Abstract

One-dimensional massive quantum particles (or 1+1-dimensional random walks) with short-ranged multi-particle interactions are studied by exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free fermions. With finite $m$-body forces (m = 3,4,...), a critical instability is found, indicating the transition to a fermionic bound state. These unbinding transitions represent new universality classes of interacting fermions relevant to polymer and membrane systems. Implications for massless fermions, e.g. in the Hubbard model, are also noted. (to appear in Phys. Rev. Lett.)