Fractionalized fermionic quantum criticality in spin-orbital Mott insulators

TL;DR

This paper investigates topological phase transitions in spin-orbital Mott insulators, revealing fractionalized fermionic quantum critical points with unique spectral properties, using analytical and numerical methods across different lattice models.

Contribution

It introduces models exhibiting fermionic quantum critical points in fractionalized Gross-Neveu universality classes with distinct topological features and critical exponents.

Findings

Critical exponents match those of Gross-Neveu universality class.

Energy spectra reflect nontrivial topology of phases.

Exact mappings enable large-scale numerical analysis.

Abstract

We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-$V$ model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ $\epsilon$-expansion and large-$N$ methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with $d^1$ electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.