Wither the sliding Luttinger liquid phase in the planar pyrochlore

TL;DR

This study investigates the zero-temperature properties of the spin-1/2 planar pyrochlore antiferromagnet, revealing that the expected sliding Luttinger liquid phase does not persist at finite inter-chain coupling, contrary to some prior theories.

Contribution

The paper provides a detailed analysis using series expansion and flow equation methods to show the absence of the sliding Luttinger liquid phase in the planar pyrochlore at finite coupling.

Findings

Critical frustration leads to a dimer phase connected to isolated dimers.

Fully frustrated inter-chain coupling is critical and prevents the sliding Luttinger liquid phase.

Results align with previous studies by Starykh et al., contradicting the existence of a sliding Luttinger liquid at finite coupling.

Abstract

Using series expansion based on the flow equation method we study the zero temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the limit of strong diagonal coupling. Starting from the limit of decoupled crossed dimers we analyze the evolution of the ground state energy and the elementary triplet excitations in terms of two coupling constants describing the inter dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the fully frustrated inter chain coupling is critical, forcing a dimer phase which adiabatically connects to the state of isolated dimers. This result is consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev. B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding Luttinger liquid phase at finite inter chain coupling.