Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube

TL;DR

This study investigates the ground state and thermodynamic behaviors of the spin-1/2 XXZ model on a pyrochlore tube, revealing phase transitions, spin-nematic tendencies, and monopole confinement characteristics using advanced numerical methods.

Contribution

It provides the first detailed analysis of the XXZ model on a pyrochlore tube, highlighting phase transitions and monopole confinement in this geometry.

Findings

Transition from spin liquid to XY ferromagnet with power-law correlations.

Evidence for spin-nematic order near certain parameter regimes.

Short monopole-anti-monopole confinement lengths, larger for negative Jx.

Abstract

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction $J_z$ and a transverse exchange interaction $J_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When $J_z$ is antiferromagnetic ($J_{z}>0$) and $J_x$ is ferromagnetic ($J_{x}<0$), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$. For $J_{z}<0$ and $J_{x}>0$, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a non-degenerate ground state with no broken symmetries and a robust energy gap. The low energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|J_{x}|$, we study the confinement of monopole-anti-monopole pairs and find that the confinement length scale is larger for $J_x<0$ than for $J_{x}>0$, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.