Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation

TL;DR

This paper explores three-dimensional quantum spin liquids in iridate models, demonstrating the stability of Kitaev QSLs at finite temperature and mapping the phase diagram using an infinite-D approximation.

Contribution

It introduces an infinite-D approximation for the Kitaev-Heisenberg model on hyperhoneycomb lattices, revealing stable 3D QSL phases and magnetic orderings.

Findings

Pure Kitaev interactions lead to an exactly solvable 3D QSL.

3D QSLs are stable at finite temperature with T_c ≈ |K|/100.

Phase diagram includes magnetically ordered and gapped QSL phases.

Abstract

Motivated by the recent synthesis of two insulating Li$_2$IrO$_3$ polymorphs, where Ir$^{4+}$ $S_{eff}$=1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $\beta$-Li$_2$IrO$_3$ hyperhoneycomb lattice and $\gamma$-Li$_2$IrO$_3$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90$^\circ$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z$_2$ flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with $T_c \approx |K|/100$. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop $\ell$ is relatively large in these structures, we construct an $\ell\rightarrow \infty$ approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint.