Tomonaga–Luttinger Spin Liquid and Kosterlitz–Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition

Abstract

In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz–Thouless transition from a gapful Lieb–Mattis phase to a gapless spin liquid phase.

On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets

“…Tomonaga-Luttinger liquids [17], and quantum phase transitions [18,19]. On the other hand, powerful methods for treating many-body systems such as Matrix Product States (MPSs) can work quasi-exactly in one dimension while allowing us to handle relatively large systems [20][21][22]; advances in digital experiments implementing these techniques and new paradigms based on variational quantum eigensolvers (VQE) in quantum chemistry [23] have prompted the search for new 0D-1D systems that can be realized in the nanoworld.…”