Quantum phase transitions in three-leg spin tubes

Abstract

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density matrix renormalization group method, strong coupling approaches and the non linear sigma model. For integer spins S, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S phase transitions. They can be accurately identified by the behavior of a non local string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions are further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S = 1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first order phase transition but at the close proximity of a tricritical point separating a gapless and a first order transition line in the phase diagram of the quantum spin tube.

20 pages, 18 figures

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Cited by in corpus (18)

• Symmetry protection of topological order in one-dimensional quantum spin systems
• Quenching the Haldane gap in spin-1 Heisenberg antiferromagnets
• Ground States of Spin-1/2 Triangular Antiferromagnets in a Magnetic Field
• Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy
• The N-Leg spin-S Heisenberg ladders: A DMRG study
• Magnetic phase diagram of the coupled triangular spin tubes for CsCrF4
• Series Expansion Analysis of a Frustrated Four-Spin-Tube
• Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields
• Exact ground states with deconfined gapless excitations for the 3 leg spin-1/2 tube
• Quantum criticality in an asymmetric three-leg spin tube: A strong rung-coupling perspective
• Quasi-fractionalization of spin in a cluster-based Haldane state supported by chirality of a triangular spin tube
• Competing phases and critical behavior in three coupled spinless Luttinger liquids
• Evidence for valence-bond pairing in a one-dimensional two-orbital system
• Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube