Quantum phase transitions between a class of symmetry protected topological states
The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT an...
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| Published in | Nuclear physics. B Vol. 896; no. C; pp. 330 - 359 |
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| Main Authors | , , , |
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| Language | English |
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01.07.2015
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| Abstract | The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional G×Z2T-symmetric SPT by a Z2T symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
•We study the phase transitions between symmetry protected topological states.•We provide a holographic interpretation.•We engineer simple lattice models. |
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| AbstractList | The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional G×Z2T-symmetric SPT by a Z2T symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
•We study the phase transitions between symmetry protected topological states.•We provide a holographic interpretation.•We engineer simple lattice models. The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional G×Z2T-symmetric SPT by a Z2T symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase. The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x ZT2-symmetric SPT by a ZT2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase. |
| Author | Tsui, Lokman Lu, Yuan-Ming Jiang, Hong-Chen Lee, Dung-Hai |
| Author_xml | – sequence: 1 givenname: Lokman surname: Tsui fullname: Tsui, Lokman email: lokman@berkeley.edu organization: Department of Physics, University of California, Berkeley, CA 94720, USA – sequence: 2 givenname: Hong-Chen surname: Jiang fullname: Jiang, Hong-Chen email: hcjiang@slac.stanford.edu organization: Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA – sequence: 3 givenname: Yuan-Ming surname: Lu fullname: Lu, Yuan-Ming email: lu.1435@osu.edu organization: Department of Physics, The Ohio State University, Columbus, OH 43212, USA – sequence: 4 givenname: Dung-Hai surname: Lee fullname: Lee, Dung-Hai email: dunghai@berkeley.edu organization: Department of Physics, University of California, Berkeley, CA 94720, USA |
| BackLink | https://www.osti.gov/biblio/1198678$$D View this record in Osti.gov |
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| Title | Quantum phase transitions between a class of symmetry protected topological states |
| URI | https://dx.doi.org/10.1016/j.nuclphysb.2015.04.020 https://www.osti.gov/biblio/1198678 https://doaj.org/article/f08ad6b22e294ba2b8f7f260a883ecec |
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