# Surprising robustness of particle-hole symmetry for composite-fermion liquids

## Abstract

Here, we report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at 1/3 and 2/3. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than *a priori* expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.

- Authors:

- Indian Institute of Science Education and Research, Pune (India)
- Pennsylvania State Univ., University Park, PA (United States)

- Publication Date:

- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)

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

- OSTI Identifier:
- 1489114

- Alternate Identifier(s):
- OSTI ID: 1394708

- Grant/Contract Number:
- SC0005042

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 12; 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; fractional quantum Hall effect; composite fermions; emergent symmetry

### Citation Formats

```
Sreejith, G. J., Zhang, Yuhe, and Jain, J. K. Surprising robustness of particle-hole symmetry for composite-fermion liquids. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.96.125149.
```

```
Sreejith, G. J., Zhang, Yuhe, & Jain, J. K. Surprising robustness of particle-hole symmetry for composite-fermion liquids. United States. doi:10.1103/PhysRevB.96.125149.
```

```
Sreejith, G. J., Zhang, Yuhe, and Jain, J. K. Mon .
"Surprising robustness of particle-hole symmetry for composite-fermion liquids". United States. doi:10.1103/PhysRevB.96.125149. https://www.osti.gov/servlets/purl/1489114.
```

```
@article{osti_1489114,
```

title = {Surprising robustness of particle-hole symmetry for composite-fermion liquids},

author = {Sreejith, G. J. and Zhang, Yuhe and Jain, J. K.},

abstractNote = {Here, we report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at 1/3 and 2/3. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.},

doi = {10.1103/PhysRevB.96.125149},

journal = {Physical Review B},

number = 12,

volume = 96,

place = {United States},

year = {2017},

month = {9}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*ν*= 5/2 as a function of κ for ideal 2D system (

*w*= 0), obtained from extrapolation from systems with up to 32 and 30 particles, respectively. (b) The energies for spin polarized (SP) states at

*ν*more »

Works referenced in this record:

##
Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations

journal, July 2011

- Thomale, Ronny; Estienne, Benoit; Regnault, Nicolas
- Physical Review B, Vol. 84, Issue 4

##
Construction of edge states in fractional quantum Hall systems by Jack polynomials

journal, April 2014

- Lee, Ki Hoon; Hu, Zi-Xiang; Wan, Xin
- Physical Review B, Vol. 89, Issue 16

##
Is the Composite Fermion a Dirac Particle?

journal, September 2015

- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3

##
New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field

journal, October 1993

- Ortiz, G.; Ceperley, D. M.; Martin, R. M.
- Physical Review Letters, Vol. 71, Issue 17

##
Paired Hall states

journal, May 1992

- Greiter, Martin; Wen, X. G.; Wilczek, Frank
- Nuclear Physics B, Vol. 374, Issue 3

##
Global Phase Diagram of the Fractional Quantum Hall Effect Arising from Repulsive Three-Body Interactions

journal, November 2010

- Wójs, Arkadiusz; Tőke, Csaba; Jain, Jainendra K.
- Physical Review Letters, Vol. 105, Issue 19

##
What Determines the Fermi Wave Vector of Composite Fermions?

journal, November 2014

- Kamburov, D.; Liu, Yang; Mueed, M. A.
- Physical Review Letters, Vol. 113, Issue 19

##
Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study

journal, December 1997

- Melik-Alaverdian, V.; Bonesteel, N. E.; Ortiz, G.
- Physical Review Letters, Vol. 79, Issue 26

##
Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

journal, April 2015

- Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry
- Physical Review X, Vol. 5, Issue 2

##
Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect

journal, October 2008

- Peterson, Michael R.; Park, Kwon; Das Sarma, S.
- Physical Review Letters, Vol. 101, Issue 15

##
Influence of Landau-level mixing on the charge-density-wave state of a two-dimensional electron gas in a strong magnetic field

journal, October 1984

- MacDonald, A. H.
- Physical Review B, Vol. 30, Issue 8

##
Nature of composite fermions and the role of particle-hole symmetry: A microscopic account

journal, June 2016

- Balram, Ajit C.; Jain, J. K.
- Physical Review B, Vol. 93, Issue 23

##
Model Fractional Quantum Hall States and Jack Polynomials

journal, June 2008

- Bernevig, B. Andrei; Haldane, F. D. M.
- Physical Review Letters, Vol. 100, Issue 24

##
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States

journal, August 1983

- Haldane, F. D. M.
- Physical Review Letters, Vol. 51, Issue 7

##
Quantum Monte Carlo simulations of solids

journal, January 2001

- Foulkes, W. M. C.; Mitas, L.; Needs, R. J.
- Reviews of Modern Physics, Vol. 73, Issue 1

##
The half-filled Landau level: The case for Dirac composite fermions

journal, April 2016

- Geraedts, S. D.; Zaletel, M. P.; Mong, R. S. K.
- Science, Vol. 352, Issue 6282

##
Maximum-density droplet to lower-density droplet transition in quantum dots

journal, July 2005

- Güçlü, A. D.; Umrigar, C. J.
- Physical Review B, Vol. 72, Issue 4

##
Fixed‐node quantum Monte Carlo for molecules ^{a) b)}

journal, December 1982

- Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J.
- The Journal of Chemical Physics, Vol. 77, Issue 11

##
Generalized quantum Hall projection Hamiltonians

journal, February 2007

- Simon, Steven H.; Rezayi, E. H.; Cooper, Nigel R.
- Physical Review B, Vol. 75, Issue 7

##
Construction of a paired wave function for spinless electrons at filling fraction $\nu =2\u22155$

journal, February 2007

- Simon, Steven H.; Rezayi, E. H.; Cooper, N. R.
- Physical Review B, Vol. 75, Issue 7

##
Transference of Fermi Contour Anisotropy to Composite Fermions

journal, July 2017

- Jo, Insun; Rosales, K. A. Villegas; Mueed, M. A.
- Physical Review Letters, Vol. 119, Issue 1

##
Infinite density matrix renormalization group for multicomponent quantum Hall systems

journal, January 2015

- Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
- Physical Review B, Vol. 91, Issue 4

##
Landau-Level Mixing and the Emergence of Pfaffian Excitations for the $5/2$ Fractional Quantum Hall Effect

journal, August 2010

- Wójs, Arkadiusz; Tőke, Csaba; Jain, Jainendra K.
- Physical Review Letters, Vol. 105, Issue 9

##
Bipartite Composite Fermion States

journal, August 2011

- Sreejith, G. J.; Tőke, C.; Wójs, A.
- Physical Review Letters, Vol. 107, Issue 8

##
Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

journal, November 2009

- Bernevig, B. Andrei; Regnault, N.
- Physical Review Letters, Vol. 103, Issue 20

##
Composite fermions and Landau-level mixing in the fractional quantum Hall effect

journal, December 1995

- Melik-Alaverdian, V.; Bonesteel, N. E.
- Physical Review B, Vol. 52, Issue 24

##
Particle-Hole Symmetry and the Pfaffian State

journal, December 2007

- Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
- Physical Review Letters, Vol. 99, Issue 23

##
Landau Level Mixing and the Ground State of the $\nu =5/2$ Quantum Hall Effect

journal, July 2017

- Rezayi, Edward H.
- Physical Review Letters, Vol. 119, Issue 2

##
Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids

journal, February 2016

- Wang, Chong; Senthil, T.
- Physical Review B, Vol. 93, Issue 8

##
Unpaired Composite Fermion, Topological Exciton, and Zero Mode

journal, September 2011

- Sreejith, G. J.; Wójs, A.; Jain, J. K.
- Physical Review Letters, Vol. 107, Issue 13

##
Particle-Hole Symmetry and the $\nu =\frac{5}{2}$ Quantum Hall State

journal, December 2007

- Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan
- Physical Review Letters, Vol. 99, Issue 23

##
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the $\nu =5/2$ Quantized Hall State

journal, March 2011

- Rezayi, Edward H.; Simon, Steven H.
- Physical Review Letters, Vol. 106, Issue 11

##
Effect of Landau level mixing on the effective interaction between electrons in the fractional quantum Hall regime

journal, September 2009

- Bishara, Waheb; Nayak, Chetan
- Physical Review B, Vol. 80, Issue 12

##
Composite Fermi liquids in the lowest Landau level

journal, December 2016

- Wang, Chong; Senthil, T.
- Physical Review B, Vol. 94, Issue 24

##
Emergent particle-hole symmetry in spinful bosonic quantum Hall systems

journal, August 2017

- Geraedts, S. D.; Repellin, C.; Wang, Chong
- Physical Review B, Vol. 96, Issue 7

##
Composite-fermion approach for the fractional quantum Hall effect

journal, July 1989

- Jain, J. K.
- Physical Review Letters, Vol. 63, Issue 2

##
Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect

journal, September 2016

- Zhang, Yuhe; Wójs, A.; Jain, J. K.
- Physical Review Letters, Vol. 117, Issue 11

##
Nonabelions in the fractional quantum hall effect

journal, August 1991

- Moore, Gregory; Read, Nicholas
- Nuclear Physics B, Vol. 360, Issue 2-3

##
More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene

journal, June 2013

- Peterson, Michael R.; Nayak, Chetan
- Physical Review B, Vol. 87, Issue 24

##
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level

journal, August 2017

- Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I.
- Physical Review X, Vol. 7, Issue 3

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*