## Numerical observation of emergent spacetime supersymmetry at quantum criticality

## Abstract

No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, the question of whether spacetime SUSY in 2 + 1 and higher dimensions can emerge in generic lattice microscopic models remains open. Here, we introduce a lattice realization of a single Dirac fermion in 2 + 1 dimensions with attractive interactions that preserves both time-reversal and chiral symmetries. By performing sign problem–free determinant quantum Monte Carlo simulations, we show that an interacting single Dirac fermion in 2 + 1 dimensions features a superconducting quantum critical point (QCP). We demonstrate that the N = 2 spacetime SUSY in 2 + 1 dimensions emerges at the superconducting QCP by showing that the fermions and bosons have identical anomalous dimensions 1/3, a hallmark of the emergent SUSY. We further show some experimental signatures that may be measured to test such emergent SUSY in candidate systems.

- Authors:

- Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Univ. of California, Berkeley, CA (United States). Dept. of Physics
- Stanford Univ., CA (United States). Dept. of Physics
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Inst. for Materials and Energy Sciences; TU Dresden (Germany). Inst. of Scientific Computing. Faculty of Mathematics
- Tsinghua Univ., Beijing (China). Inst. for Advanced Study. State Key Lab. of Low Dimensional Quantum Physics

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States); Tsinghua Univ., Beijing (China); TU Dresden (Germany)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Gordon and Betty Moore Foundation (United States); Ministry of Science and Technology (MOST) (China); National Natural Science Foundation of China (NNSFC); Alexander von Humboldt Foundation (Germany)

- OSTI Identifier:
- 1490443

- Grant/Contract Number:
- AC02-76SF00515; GBMF4302; 2016YFA0301001; 2018YFA0305604; 11474175

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Science Advances

- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 11; Journal ID: ISSN 2375-2548

- Publisher:
- AAAS

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Li, Zi-Xiang, Vaezi, Abolhassan, Mendl, Christian B., and Yao, Hong. Numerical observation of emergent spacetime supersymmetry at quantum criticality. United States: N. p., 2018.
Web. doi:10.1126/sciadv.aau1463.
```

```
Li, Zi-Xiang, Vaezi, Abolhassan, Mendl, Christian B., & Yao, Hong. Numerical observation of emergent spacetime supersymmetry at quantum criticality. United States. doi:10.1126/sciadv.aau1463.
```

```
Li, Zi-Xiang, Vaezi, Abolhassan, Mendl, Christian B., and Yao, Hong. Fri .
"Numerical observation of emergent spacetime supersymmetry at quantum criticality". United States. doi:10.1126/sciadv.aau1463. https://www.osti.gov/servlets/purl/1490443.
```

```
@article{osti_1490443,
```

title = {Numerical observation of emergent spacetime supersymmetry at quantum criticality},

author = {Li, Zi-Xiang and Vaezi, Abolhassan and Mendl, Christian B. and Yao, Hong},

abstractNote = {No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, the question of whether spacetime SUSY in 2 + 1 and higher dimensions can emerge in generic lattice microscopic models remains open. Here, we introduce a lattice realization of a single Dirac fermion in 2 + 1 dimensions with attractive interactions that preserves both time-reversal and chiral symmetries. By performing sign problem–free determinant quantum Monte Carlo simulations, we show that an interacting single Dirac fermion in 2 + 1 dimensions features a superconducting quantum critical point (QCP). We demonstrate that the N = 2 spacetime SUSY in 2 + 1 dimensions emerges at the superconducting QCP by showing that the fermions and bosons have identical anomalous dimensions 1/3, a hallmark of the emergent SUSY. We further show some experimental signatures that may be measured to test such emergent SUSY in candidate systems.},

doi = {10.1126/sciadv.aau1463},

journal = {Science Advances},

number = 11,

volume = 4,

place = {United States},

year = {2018},

month = {11}

}

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Works referenced in this record:

##
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