# Local Two-Body Parent Hamiltonians for the Entire Jain Sequence

## Abstract

Using an algebra of second-quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor $n/(2n\mathsf{p}+1)$, with integer $n$ and (half-)integer $\mathsf{p}$. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish the organizing “entangled Pauli principle” behind the resulting zero mode paradigm and unveil an emergent $\mathrm{SU}\left(n\right)$ symmetry characteristic of the fixed point physics of the Jain quantum Hall fluid.

- Authors:

- Publication Date:

- Research Org.:
- Indiana Univ., Bloomington, IN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); European Research Council (ERC)

- OSTI Identifier:
- 1619877

- Alternate Identifier(s):
- OSTI ID: 1630820

- Grant/Contract Number:
- SC0020343; ERS-2018-SYG 810451

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 19; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Bandyopadhyay, Sumanta, Ortiz, Gerardo, Nussinov, Zohar, and Seidel, Alexander. Local Two-Body Parent Hamiltonians for the Entire Jain Sequence. United States: N. p., 2020.
Web. doi:10.1103/PhysRevLett.124.196803.
```

```
Bandyopadhyay, Sumanta, Ortiz, Gerardo, Nussinov, Zohar, & Seidel, Alexander. Local Two-Body Parent Hamiltonians for the Entire Jain Sequence. United States. https://doi.org/10.1103/PhysRevLett.124.196803
```

```
Bandyopadhyay, Sumanta, Ortiz, Gerardo, Nussinov, Zohar, and Seidel, Alexander. Fri .
"Local Two-Body Parent Hamiltonians for the Entire Jain Sequence". United States. https://doi.org/10.1103/PhysRevLett.124.196803.
```

```
@article{osti_1619877,
```

title = {Local Two-Body Parent Hamiltonians for the Entire Jain Sequence},

author = {Bandyopadhyay, Sumanta and Ortiz, Gerardo and Nussinov, Zohar and Seidel, Alexander},

abstractNote = {Using an algebra of second-quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor n/(2np+1), with integer n and (half-)integer p. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish the organizing “entangled Pauli principle” behind the resulting zero mode paradigm and unveil an emergent SU(n) symmetry characteristic of the fixed point physics of the Jain quantum Hall fluid.},

doi = {10.1103/PhysRevLett.124.196803},

journal = {Physical Review Letters},

number = 19,

volume = 124,

place = {United States},

year = {2020},

month = {5}

}

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