Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

Journal Article · 01 August 2023 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.15.2.043 · OSTI ID:1993535

Tanhayi Ahari, Mostafa ^[1]; Bandyopadhyay, Sumanta ^[2]; Nussinov, Zohar ^[3]; Seidel, Alexander ^[3]; Ortiz, Gerardo ^[4]

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1. Indiana University Bloomington, University of California Los Angeles
2. Nordic Institute for Theoretical Physics, Washington University in St. Louis
3. Washington University in St. Louis
4. Indiana University Bloomington

We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor \nu=2/3 $\nu =2/3$ . The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M $M$ -clustering property within any given number of Landau levels, that is, wave functions with M $M$ th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M=3 $M=3$ case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

• Research Organization: Indiana Univ., Bloomington, IN (United States); Univ. of California, Los Angeles, CA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0012190; SC0020343
• OSTI ID: 1993535
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 15; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English