Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks

TL;DR

This paper uses tensor network simulations to explore the thermodynamics and phase diagrams of 3D Kitaev and Kitaev-Heisenberg models on hyperhoneycomb and hyperoctagon lattices, revealing fractionalization, topological features, and phase transitions.

Contribution

It provides the first detailed tensor network analysis of 3D Kitaev models at finite temperature, mapping phase diagrams and characterizing topological and magnetic phases.

Findings

Identification of spin fractionalization into Majorana fermions and gauge fields at different temperatures.

Demonstration of topological features such as Weyl nodes and non-zero Chern numbers in the QSL phase.

Observation of standard Landau phase transition in magnetically ordered regions of the Kitaev-Heisenberg model.

Abstract

We study the 3D Kitaev and Kitaev-Heisenberg models respectively on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph Projected Entangled-Pair States (gPEPS). We map out the TN phase diagrams of the models and characterize their underlying gapped and gapless phases both at zero and finite temperature. In particular, we demonstrate how cooling down the hyperhoneycomb system from high-temperature leads to fractionalization of spins to itinerant Majorana fermions and gauge fields that occurs in two separate temperature regimes, leaving their fingerprint on specific heat as a double-peak feature as well as on other quantities such as the thermal entropy, spin-spin correlations and bond entropy. Using the Majorana representation of the Kitaev model, we further show that the low-temperature thermal transition to the Kitaev quantum spin liquid (QSL) phase is associated with the non-trivial Majorana band topology and the presence of Weyl nodes, which manifests itself via non-vanishing Chern number and finite thermal Hall conductivity. Beyond the pure Kitaev limit, we study the 3D Kitaev-Heisenberg (KH) model on the hyperoctagon lattice and extract the full phase diagram for different Heisenberg couplings. We further explore the thermodynamic properties of the magnetically-ordered regions in the KH model and show that, in contrast to the QSL phase, here the thermal phase transition follows the standard Landau symmetry-breaking theory.