# Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

## Abstract

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.

- Authors:

- Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS); Univ. of Alabama, Tuscaloosa, AL (United States)
- Princeton Univ., NJ (United States)
- Univ. of Alberta, Edmonton, AB (Canada); Canadian Inst. for Advanced Research, Toronto, ON (Canada)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- Natural Sciences and Engineering Research Council of Canada (NSERC); University of Alberta; Canadian Institute for Advanced Research (CIFAR); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1339548

- Alternate Identifier(s):
- OSTI ID: 1306704

- Grant/Contract Number:
- AC02-06CH11357; FG02-05ER46201; AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 117; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Chen, Cheng-Chien, Muechler, Lukas, Car, Roberto, Neupert, Titus, and Maciejko, Joseph.
```*Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevLett.117.096405.

```
Chen, Cheng-Chien, Muechler, Lukas, Car, Roberto, Neupert, Titus, & Maciejko, Joseph.
```*Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model*. United States. doi:10.1103/PhysRevLett.117.096405.

```
Chen, Cheng-Chien, Muechler, Lukas, Car, Roberto, Neupert, Titus, and Maciejko, Joseph. Thu .
"Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model". United States.
doi:10.1103/PhysRevLett.117.096405. https://www.osti.gov/servlets/purl/1339548.
```

```
@article{osti_1339548,
```

title = {Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model},

author = {Chen, Cheng-Chien and Muechler, Lukas and Car, Roberto and Neupert, Titus and Maciejko, Joseph},

abstractNote = {We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.},

doi = {10.1103/PhysRevLett.117.096405},

journal = {Physical Review Letters},

number = ,

volume = 117,

place = {United States},

year = {Thu Aug 25 00:00:00 EDT 2016},

month = {Thu Aug 25 00:00:00 EDT 2016}

}

*Citation information provided by*

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Web of Science

Works referenced in this record:

##
The quantum spin Hall effect and topological insulators

journal, January 2010

- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Physics Today, Vol. 63, Issue 1, p. 33-38