Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function

Pakrouski, Kiryl

doi:10.1103/physrevb.104.245306

Title: Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function

Journal Article · 29 December 2021 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.104.245306 · OSTI ID:1979694

^[1]

Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland); Princeton University, NJ (United States); OSTI

We present two two-body Hamiltonians that approximate the exact particle-hole Pfaffian wave function with their ground states for all the system sizes where this wave function has been numerically constructed to date. The approximate wave functions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimization procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a noninteracting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the particle-hole Pfaffian. Here we diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the particle-hole Pfaffian shift appears energetically more favorable. The possibility to interpret the data in terms of composite fermions is discussed.

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Research Organization:: Princeton University, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Swiss National Science Foundation

Grant/Contract Number:: SC0002140

OSTI ID:: 1979694

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 104; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (64)

Nonabelions in the fractional quantum hall effect Moore, Gregory; Read, Nicholas Nuclear Physics B, Vol. 360, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90407-O	journal	August 1991
Quantum many-body scars and weak breaking of ergodicity Serbyn, Maksym; Abanin, Dmitry A.; Papić, Zlatko Nature Physics, Vol. 17, Issue 6 https://doi.org/10.1038/s41567-021-01230-2	journal	May 2021
Observation of half-integer thermal Hall conductance Banerjee, Mitali; Heiblum, Moty; Umansky, Vladimir Nature, Vol. 559, Issue 7713 https://doi.org/10.1038/s41586-018-0184-1	journal	June 2018
Model interactions for Pfaffian paired states based on Chern-Simons field theory description Đurđević, Stevan; Milovanović, Milica V. Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevB.100.195303	journal	November 2019
Energetics of Pfaffian–anti-Pfaffian domains Simon, Steven H.; Ippoliti, Matteo; Zaletel, Michael P. Physical Review B, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevB.101.041302	journal	January 2020
Particle-hole Pfaffian order in a translationally and rotationally invariant system Sun, Chen; Ma, Ken K. W.; Feldman, D. E. Physical Review B, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevB.102.121303	journal	September 2020
Large-scale simulations of particle-hole-symmetric Pfaffian trial wave functions Yutushui, Mykhailo; Mross, David F. Physical Review B, Vol. 102, Issue 19 https://doi.org/10.1103/PhysRevB.102.195153	journal	November 2020
Partial equilibration of anti-Pfaffian edge modes at ν = 5 / 2 Asasi, Hamed; Mulligan, Michael Physical Review B, Vol. 102, Issue 20 https://doi.org/10.1103/PhysRevB.102.205104	journal	November 2020
Stability of the particle-hole Pfaffian state and the 5 2 -fractional quantum Hall effect Rezayi, Edward H.; Pakrouski, Kiryl; Haldane, F. D. M. Physical Review B, Vol. 104, Issue 8 https://doi.org/10.1103/PhysRevB.104.L081407	journal	August 2021
Magneto-roton theory of collective excitations in the fractional quantum Hall effect Girvin, S. M.; MacDonald, A. H.; Platzman, P. M. Physical Review B, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevB.33.2481	journal	February 1986
Configuration-interaction calculations on the fractional quantum Hall effect Fano, G.; Ortolani, F.; Colombo, E. Physical Review B, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevB.34.2670	journal	August 1986
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces Wen, X. G.; Niu, Q. Physical Review B, Vol. 41, Issue 13 https://doi.org/10.1103/PhysRevB.41.9377	journal	May 1990
Fractional quantum Hall effect at ν = 5 ∕ 2 : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model Wan, Xin; Hu, Zi-Xiang; Rezayi, E. H. Physical Review B, Vol. 77, Issue 16 https://doi.org/10.1103/PhysRevB.77.165316	journal	April 2008
Fractional quantum Hall states at 1 3 and 5 2 filling: Density-matrix renormalization group calculations Zhao, Jize; Sheng, D. N.; Haldane, F. D. M. Physical Review B, Vol. 83, Issue 19 https://doi.org/10.1103/PhysRevB.83.195135	journal	May 2011
Landau level mixing in the perturbative limit Simon, Steven H.; Rezayi, Edward H. Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155426	journal	April 2013
More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene Peterson, Michael R.; Nayak, Chetan Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.245129	journal	June 2013
Landau level mixing and the fractional quantum Hall effect Sodemann, I.; MacDonald, A. H. Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.245425	journal	June 2013
Infinite density matrix renormalization group for multicomponent quantum Hall systems Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045115	journal	January 2015
Interpretation of thermal conductance of the ν = 5 / 2 edge Simon, Steven H. Physical Review B, Vol. 97, Issue 12 https://doi.org/10.1103/PhysRevB.97.121406	journal	March 2018
Theory of the disordered ν = 5 2 quantum thermal Hall state: Emergent symmetry and phase diagram Lian, Biao; Wang, Juven Physical Review B, Vol. 97, Issue 16 https://doi.org/10.1103/PhysRevB.97.165124	journal	April 2018
Parton construction of a wave function in the anti-Pfaffian phase Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S. Physical Review B, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevB.98.035127	journal	July 2018
Topological order from disorder and the quantized Hall thermal metal: Possible applications to the ν = 5 / 2 state Wang, Chong; Vishwanath, Ashvin; Halperin, Bertrand I. Physical Review B, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevB.98.045112	journal	July 2018
Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian Mishmash, Ryan V.; Mross, David F.; Alicea, Jason Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.081107	journal	August 2018
Method to identify parent Hamiltonians for trial states Greiter, Martin; Schnells, Vera; Thomale, Ronny Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.081113	journal	August 2018
Paired states at 5/2: Particle-hole Pfaffian and particle-hole symmetry breaking Antonić, L.; Vučičević, J.; Milovanović, M. V. Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115107	journal	September 2018
Comment on “Interpretation of thermal conductance of the ν = 5 / 2 edge” Feldman, D. E. Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevB.98.167401	journal	October 2018
Reply to “Comment on ‘Interpretation of thermal conductance of the ν = 5 / 2 edge' ” Simon, Steven H. Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevB.98.167402	journal	October 2018
Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect Ma, Ken K. W.; Feldman, D. E. Physical Review B, Vol. 99, Issue 8 https://doi.org/10.1103/PhysRevB.99.085309	journal	February 2019
Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States Feiguin, A. E.; Rezayi, E.; Nayak, C. Physical Review Letters, Vol. 100, Issue 16 https://doi.org/10.1103/PhysRevLett.100.166803	journal	April 2008
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States Li, Hui; Haldane, F. D. M. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.010504	journal	July 2008
Finite-Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wave Function Overlap and Topological Degeneracy Peterson, Michael. R.; Jolicoeur, Th.; Das Sarma, S. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.016807	journal	July 2008
Fractional Quantum Hall State at ν = 5 2 and the Moore-Read Pfaffian Storni, M.; Morf, R. H.; Das Sarma, S. Physical Review Letters, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevLett.104.076803	journal	February 2010
Landau-Level Mixing and the Emergence of Pfaffian Excitations for the 5 / 2 Fractional Quantum Hall Effect Wójs, Arkadiusz; Tőke, Csaba; Jain, Jainendra K. Physical Review Letters, Vol. 105, Issue 9 https://doi.org/10.1103/PhysRevLett.105.096802	journal	August 2010
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the ν = 5 / 2 Quantized Hall State Rezayi, Edward H.; Simon, Steven H. Physical Review Letters, Vol. 106, Issue 11 https://doi.org/10.1103/PhysRevLett.106.116801	journal	March 2011
Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry Zucker, P. T.; Feldman, D. E. Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.096802	journal	August 2016
Landau Level Mixing and the Ground State of the ν = 5 / 2 Quantum Hall Effect Rezayi, Edward H. Physical Review Letters, Vol. 119, Issue 2 https://doi.org/10.1103/PhysRevLett.119.026801	journal	July 2017
Theory of Disorder-Induced Half-Integer Thermal Hall Conductance Mross, David F.; Oreg, Yuval; Stern, Ady Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026801	journal	July 2018
Quantum Machine Learning in Feature Hilbert Spaces Schuld, Maria; Killoran, Nathan Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.040504	journal	February 2019
Partial Equilibration of the Anti-Pfaffian Edge due to Majorana Disorder Simon, Steven H.; Rosenow, Bernd Physical Review Letters, Vol. 124, Issue 12 https://doi.org/10.1103/PhysRevLett.124.126801	journal	March 2020
Thermal Equilibration on the Edges of Topological Liquids Ma, Ken K. W.; Feldman, D. E. Physical Review Letters, Vol. 125, Issue 1 https://doi.org/10.1103/PhysRevLett.125.016801	journal	July 2020
Noise on the non-Abelian ν = 5 / 2 Fractional Quantum Hall Edge Park, Jinhong; Spånslätt, Christian; Gefen, Yuval Physical Review Letters, Vol. 125, Issue 15 https://doi.org/10.1103/PhysRevLett.125.157702	journal	October 2020
Many-Body Scars as a Group Invariant Sector of Hilbert Space Pakrouski, K.; Pallegar, P. N.; Popov, F. K. Physical Review Letters, Vol. 125, Issue 23 https://doi.org/10.1103/PhysRevLett.125.230602	journal	December 2020
Temperature Enhancement of Thermal Hall Conductance Quantization Fulga, I. C.; Oreg, Yuval; Mirlin, Alexander D. Physical Review Letters, Vol. 125, Issue 23 https://doi.org/10.1103/PhysRevLett.125.236802	journal	December 2020
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States Haldane, F. D. M. Physical Review Letters, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevLett.51.605	journal	August 1983
Collective-Excitation Gap in the Fractional Quantum Hall Effect Girvin, S. M.; MacDonald, A. H.; Platzman, P. M. Physical Review Letters, Vol. 54, Issue 6 https://doi.org/10.1103/PhysRevLett.54.581	journal	February 1985
Observation of an even-denominator quantum number in the fractional quantum Hall effect Willett, R.; Eisenstein, J. P.; Störmer, H. L. Physical Review Letters, Vol. 59, Issue 15 https://doi.org/10.1103/PhysRevLett.59.1776	journal	October 1987
Composite-fermion approach for the fractional quantum Hall effect Jain, J. K. Physical Review Letters, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevLett.63.199	journal	July 1989
Transition from Quantum Hall to Compressible States in the Second Landau Level: New Light on the ν = 5 / 2 Enigma Morf, R. H. Physical Review Letters, Vol. 80, Issue 7 https://doi.org/10.1103/PhysRevLett.80.1505	journal	February 1998
Incompressible Paired Hall State, Stripe Order, and the Composite Fermion Liquid Phase in Half-Filled Landau Levels Rezayi, E. H.; Haldane, F. D. M. Physical Review Letters, Vol. 84, Issue 20 https://doi.org/10.1103/PhysRevLett.84.4685	journal	May 2000
Understanding the 5 2 Fractional Quantum Hall Effect without the Pfaffian Wave Function Tőke, Csaba; Jain, Jainendra K. Physical Review Letters, Vol. 96, Issue 24 https://doi.org/10.1103/PhysRevLett.96.246805	journal	June 2006
Non-Abelian States with Negative Flux: A New Series of Quantum Hall States Jolicoeur, Th. Physical Review Letters, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevLett.99.036805	journal	July 2007
Particle-Hole Symmetry and the Pfaffian State Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236806	journal	December 2007
Particle-Hole Symmetry and the ν = 5 2 Quantum Hall State Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236807	journal	December 2007
Group theoretic approach to many-body scar states in fermionic lattice models Pakrouski, K.; Pallegar, P. N.; Popov, F. K. Physical Review Research, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevResearch.3.043156	journal	December 2021
Phase Diagram of the ν = 5 / 2 Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry Physical Review X, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevX.5.021004	journal	April 2015
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions Chertkov, Eli; Clark, Bryan K. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031029	journal	July 2018
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Quantum Hall physics: Hierarchies and conformal field theory techniques Hansson, T. H.; Hermanns, M.; Simon, S. H. Reviews of Modern Physics, Vol. 89, Issue 2 https://doi.org/10.1103/RevModPhys.89.025005	journal	May 2017
Topological Orders in Rigid States Wen, X. G. International Journal of Modern Physics B, Vol. 04, Issue 02 https://doi.org/10.1142/S0217979290000139	journal	February 1990
Theory of the edge States in Fractional Quantum hall Effects Wen, Xiao-Gang International Journal of Modern Physics B, Vol. 06, Issue 10 https://doi.org/10.1142/S0217979292000840	journal	May 1992
Pfaffian paired states for half-integer fractional quantum Hall effect Milovanović, M. V.; Djurdjević, S.; Vučičević, J. Modern Physics Letters B, Vol. 34, Issue 21 https://doi.org/10.1142/S0217984920300045	journal	July 2020
Determining a local Hamiltonian from a single eigenstate Qi, Xiao-Liang; Ranard, Daniel Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-08-159	journal	July 2019
Automatic design of Hamiltonians Pakrouski, Kiryl Quantum, Vol. 4 https://doi.org/10.22331/q-2020-09-02-315	journal	September 2020

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Title: Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function

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