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arXiv:1812.04656 · Physical review. B./Physical review. B

Anomalous domain wall condensation in a modified Ising chain

Gertian Roose, Laurens Vanderstraeten, Jutho Haegeman, Nick Bultinck

Published May 20, 2019• 6 citations
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Abstract

We construct a one-dimensional local spin Hamiltonian with an intrinsically nonlocal, and therefore anomalous, global ${\mathbb{Z}}_{2}$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and contains a parameter that can be tuned to spontaneously break the nonlocal ${\mathbb{Z}}_{2}$ symmetry. The Hamiltonian is constructed to capture the unconventional properties of the domain walls in the symmetry-broken phase. Using uniform matrix product states, we obtain the phase diagram that results from condensing the domain walls. We find that the complete phase diagram includes a gapless phase that is separated from the ordered ferromagnetic phase by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered antiferromagnetic phase by a first-order phase transition.

DOI
10.1103/physrevb.99.195132

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We study the anisotropic Heisenberg (XYZ)(\mathrm{XYZ})(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 nontrivial fixed point at a certain value of the XY\mathrm{XY}XY anisotropy a and the magnetic field h. Hence there is a line of critical points in the (a,h)(a,h)(a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flip transition; it separates two gapped phases in one of which the Z2{Z}_{2}Z2​ symmetry of the Hamiltonian is broken. Our study has a bearing on one of the transitions of the axial next-nearest neighbor Ising chain in a transverse magnetic field. We also discuss the properties of the model when the magnetic field is increased further, in particular, the disorder line on which the ground state is a direct product of single spin states.