Breakdown of order-fractionalization in the CPT model

TL;DR

This paper analyzes the phase transitions and fractionalization phenomena in the half-filled CPT model, revealing a quantum critical point, thermal breakdown scales, and a decoupled orbital liquid phase.

Contribution

It provides the first detailed analysis of the CPT model's phase diagram, identifying critical points and thermal effects on order fractionalization.

Findings

Identified a quantum critical point at J_c between superconducting and Kondo insulator phases.

Estimated thermal energy scales for the breakdown of order fractionalization.

Discovered a decoupled Kitaev orbital liquid phase at large J.

Abstract

We present an analysis of the half-filled CPT model, an analytically tractable Kondo lattice model with Yao-Lee spin-spin interactions on a 3D hyperoctagon lattice, proposed by Coleman, Panigrahi, and Tsvelik. Previous studies have established that the CPT model exhibits odd-frequency triplet superconductivity and order fractionalization. Through asymptotic analyses in the small $J$ and large $J$ Kondo coupling limits, we identify a quantum critical point at $J_c$, marking a transition from a superconductor to a Kondo insulator. By estimating the vison gap energy to account for thermal gauge fluctuations, we determine the energy scales governing the thermal breakdown of order fractionalization. Moreover, at large $J$ the Kondo insulator undergoes orbital decoupling, leading to the formation of a decoupled Kitaev orbital liquid. These findings and analogies with the $\mathbb{Z}_2$-gauged $XY$ model lead us to propose a tentative phase diagram for the CPT model at half-filling.