Emergent Wigner magnon crystals in a fully frustrated Heisenberg four-leg tube

Abstract

The ground state, magnetization curves, low-temperature thermodynamics, and heat-engine performance of the fully frustrated spin-$1/2$ Heisenberg four-leg tube with antiferromagnetic inter- and intra-plaquette coupling constants J1 and J2 are examined using exact diagonalization, density matrix renormalization group, and localized-magnon theory. In the unfrustrated to weakly frustrated regime J2/J1 << 2, the system exhibits a continuous field-driven quantum phase transition between the gapped Haldane phase and a gapless Tomonaga-Luttinger quantum spin liquid. In the highly frustrated regime J2/J1 > 2, the system contrarily displays discontinuous field-driven quantum phase transitions between the Wigner magnon crystals, which are manifested in zero-temperature magnetization curves as intermediate plateaus at zero, one-quarter, one-half, and three-quarters of the saturation magnetization. The low-temperature magnetic and thermodynamic properties in this regime are accurately captured by an effective interacting lattice-gas model of two monomer quasi-particle species constructed from localized one- and two-magnon states. Finally, we explore a quantum Stirling heat engine using the fully frustrated four-leg tube as the working medium. The work output and efficiency are strongly suppressed near discontinuous field-induced transitions and reach pronounced local maxima well inside the stability regions of the Wigner magnon crystals.