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Journal Article

Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection


Fuji,  Yohei
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Fuji, Y. (2016). Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection. Physical Review B, 93(10): 104425. doi:10.1103/PhysRevB.93.104425.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-3FD9-F
We investigate valence-bond-solid (VBS) phases in one-dimensional spin systems by an effective field theory developed by Schulz [Phys. Rev. B 34, 6372 (1986)]. While the distinction among the VBS phases is often understood in terms of different entanglement structures protected by certain symmetries, we adopt a different but more fundamental point of view, that is, different VBS phases are separated by a gap closing under certain symmetries. In this way, the effective field theory reproduces the known three symmetries: time reversal, bond-centered inversion, and dihedral group of pi spin rotations. It also predicts that there exists another symmetry: site-centered inversion combined with a spin rotation by pi. We demonstrate that the last symmetry gives distinct trivial phases, which cannot be characterized by their entanglement structure, in terms of a simple perturbative analysis in a spin chain. We also discuss several applications of the effective field theory to the phase transitions among VBS phases in microscopic models and an extension of the Lieb-Schultz-Mattis theorem to non-translational-invariant systems.