Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions
Abstract
In this work, using the decorated domain wall procedure, we construct finite-depth local unitaries that realize fermionic symmetry-protected topological (SPT) phases. This results in explicit full commuting projector Hamiltonians, where "full" implies the fact that the ground state as well as all excited states of these Hamiltonians realize the nontrivial SPT phase. We begin by constructing explicit examples of 1+1D phases protected by the symmetry group G=$$\mathbb{Z}_2^T$$×$$\mathbb{Z}_2^F$$, which also has a free fermion realization in class BDI, and by the symmetry group G=$$\mathbb{Z}_4$$×$$\mathbb{Z}_4^F$$, which does not. We then turn to 2+1D, and construct the square roots of the Levin-Gu bosonic SPT phase, protected by $$\mathbb{Z}_2$$×$$\mathbb{Z}_2^F$$ symmetry, in a concrete model of fermions and spins on the triangular lattice. Edge states and the anomalous symmetry action on them are explicitly derived. Although this phase has a free fermion representation as two copies of p+ ip superconductors combined with their p- ip counterparts with a different symmetry charge, the full set of commuting projectors is only realized in the strongly interacting version, which also implies that it admits a many-body localized realization.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1571111
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 16; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Tantivasadakarn, Nathanan, and Vishwanath, Ashvin. Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions. United States: N. p., 2018.
Web. doi:10.1103/physrevb.98.165104.
Tantivasadakarn, Nathanan, & Vishwanath, Ashvin. Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions. United States. https://doi.org/10.1103/physrevb.98.165104
Tantivasadakarn, Nathanan, and Vishwanath, Ashvin. Tue .
"Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions". United States. https://doi.org/10.1103/physrevb.98.165104. https://www.osti.gov/servlets/purl/1571111.
@article{osti_1571111,
title = {Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions},
author = {Tantivasadakarn, Nathanan and Vishwanath, Ashvin},
abstractNote = {In this work, using the decorated domain wall procedure, we construct finite-depth local unitaries that realize fermionic symmetry-protected topological (SPT) phases. This results in explicit full commuting projector Hamiltonians, where "full" implies the fact that the ground state as well as all excited states of these Hamiltonians realize the nontrivial SPT phase. We begin by constructing explicit examples of 1+1D phases protected by the symmetry group G=$\mathbb{Z}_2^T$×$\mathbb{Z}_2^F$, which also has a free fermion realization in class BDI, and by the symmetry group G=$\mathbb{Z}_4$×$\mathbb{Z}_4^F$, which does not. We then turn to 2+1D, and construct the square roots of the Levin-Gu bosonic SPT phase, protected by $\mathbb{Z}_2$×$\mathbb{Z}_2^F$ symmetry, in a concrete model of fermions and spins on the triangular lattice. Edge states and the anomalous symmetry action on them are explicitly derived. Although this phase has a free fermion representation as two copies of p+ip superconductors combined with their p-ip counterparts with a different symmetry charge, the full set of commuting projectors is only realized in the strongly interacting version, which also implies that it admits a many-body localized realization.},
doi = {10.1103/physrevb.98.165104},
url = {https://www.osti.gov/biblio/1571111},
journal = {Physical Review B},
issn = {2469-9950},
number = 16,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}
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