Dynamic properties of the spin-1/2 XY chain with three-site interactions

Abstract

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.

28 pages, 10 fugures

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• Magnetism-driven ferroelectricity in spin-1/2 $XY$ chains
• Exact solution of a spin-1/2 $XX$ chain with three-site interactions in a random transverse field: Influence of randomness on quantum phase transition
• The three site interacting spin chain in staggered field: Fidelity vs Loschmidt echo
• Emergent phases in a compass chain with multisite interactions
• Enhancement of non-equilibrium thermal quantum discord and entanglement of a three-spin XX chain by multi-spin interaction and external magnetic field
• Energy dynamics in a generalized compass chain
• Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model
• Orbital antiferroelectricity and higher dimensional magnetoelectric order in the spin-$1/2$ XX chain extended with three-spin interactions
• Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Heisenberg spin chains with additional isotropic three-site exchange interactions
• Quantum phase transitions in the alternating XY chain with three-site interactions