## Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

## Abstract

Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. With this work, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry.We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Moreover, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Hence, we identify the liquid phase as a quantum Hall phase, which provides a “proof-of-principle” demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.

- Authors:

- California State Univ. Northridge (CSUN), Northridge, CA (United States)
- Florida State Univ., Tallahassee, FL (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- California State Univ. Northridge (CSUN), Northridge, CA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1505728

- Alternate Identifier(s):
- OSTI ID: 1328624

- Grant/Contract Number:
- FG02-06ER46305

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 9; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, and Sheng, D. N. Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice. United States: N. p., 2016.
Web. doi:10.1103/physrevlett.117.096402.
```

```
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, & Sheng, D. N. Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice. United States. doi:10.1103/physrevlett.117.096402.
```

```
Zhu, W., Gong, Shou-Shu, Zeng, Tian-Sheng, Fu, Liang, and Sheng, D. N. Tue .
"Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice". United States. doi:10.1103/physrevlett.117.096402. https://www.osti.gov/servlets/purl/1505728.
```

```
@article{osti_1505728,
```

title = {Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice},

author = {Zhu, W. and Gong, Shou-Shu and Zeng, Tian-Sheng and Fu, Liang and Sheng, D. N.},

abstractNote = {Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. With this work, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry.We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Moreover, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Hence, we identify the liquid phase as a quantum Hall phase, which provides a “proof-of-principle” demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.},

doi = {10.1103/physrevlett.117.096402},

journal = {Physical Review Letters},

number = 9,

volume = 117,

place = {United States},

year = {2016},

month = {8}

}

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Works referenced in this record:

##
*Colloquium*: Topological insulators

journal, November 2010

- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067