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arXiv:cond-mat/0208216

Gapless Phase in the XYZ Spin-1/2 Chain in a Magnetic Field and the Quantum ANNNI Chain

Amit Dutta, Diptiman Sen

Published Aug 12, 2002• 0 citations
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Abstract

We study the XYZ spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the plane (a,h) on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line separates a gapped commensurate phase from a gapped incommensurate phase. Our study explains why the floating phase of the axial next-nearest neighbor Ising (ANNNI) chain in a transverse magnetic field is only a line, as shown by recent numerical studies.

DOI
10.48550/arxiv.cond-mat/0208216

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The finite field para-ferrimagnetic phase transition in the axial next-nearest-neighbor Ising (ANNNI) model is studied by using the linear perturbation real space renormalization group transformation. The method is examined in systems of ferromagnetic and antiferromagnetic Ising chains coupled by ferromagnetic interactions in the longitudinal field. As one would expect, the external field in the first case destroys the continuous phase transition and in the second shifts the critical point toward a lower temperature according to the square law. For the ferromagnetic chains coupled by the competing interchain nearest-neighbor J(1) < 0 and next-nearest-neighbor J(2) < 0 interactions, the external field changes the character of the phase transition from continuous to discontinuous. However, it has been found that for the ratio J(2)/J(1) around 0.5 there is a critical value of the field for which an isolated critical point exists. The temperature dependences of the specific heat for several values of J(2)/J(1) and the external field are presented.