Series Expansion Analysis of a Frustrated Four-Spin-Tube

We study the magnetism of a frustrated four-leg spin-1/2 ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung-coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First we show that frustration destabilizes the spin-gap phase of the FFST which is adiabatically connected to the limit of decoupled rung singlets, leading to a first order quantum phase transition at finite inter-rung coupling. Second, we show that apart from the well-know triplon branch of spin-ladders, the FFST sustains additional elementary excitations, including a singlon, and additional triplons. Finally we find, that in the two-particle sector the FFST exhibits collective (anti)bound states similar to two-leg ladders, however with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.