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- Ahari, Mostafa Tanhayi, et al.
(author)
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Partons as unique ground states of quantum Hall parent Hamiltonians : The case of Fibonacci anyons
- 2023
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In: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 15:2
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Journal article (peer-reviewed)abstract
- 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 ν = 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-clustering property within any given number of Landau levels, that is, wave functions with Mth-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the 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.
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| 2. |
- Bandyopadhyay, Sumanta, et al.
(author)
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Local Two-Body Parent Hamiltonians for the Entire Jain Sequence
- 2020
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In: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 124:19
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Journal article (peer-reviewed)abstract
- 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.
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| 3. |
- Nussinov, Zohar, et al.
(author)
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Mapping between finite temperature classical and zero temperature quantum systems : Quantum critical jamming and quantum dynamical heterogeneities
- 2013
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In: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 87:18, s. 184202-
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Journal article (peer-reviewed)abstract
- Many electronic systems (e. g., the cuprate superconductors and heavy fermions) exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are some empirical suggestions of particular increasing length scales that accompany such transitions in some cases, this identification is not universal and in numerous instances no large correlation length is evident. To better understand, as a matter of principle, such behavior in quantum systems, we extend a known mapping (earlier studied in stochastic or supersymmetric quantum mechanics) between finite temperature classical Fokker-Planck systems and related quantum systems at zero temperature to include general nonequilibrium dynamics. Unlike Feynman mappings or stochastic quantization methods in field theories (as well as more recent holographic type dualities), the classical systems that we consider and their quantum duals reside in the same number of space-time dimensions. The upshot of our very broad and rigorous result is that a Wick rotation exactly relates (i) the dynamics in general finite temperature classical dissipative systems to (ii) zero temperature dynamics in the corresponding dual many-body quantum systems. Using this correspondence, we illustrate that, even in the absence of imposed disorder, many continuum quantum fluid systems (and possible lattice counterparts) may exhibit a zero-point quantum dynamical heterogeneity wherein the dynamics, at a given instant, is spatially nonuniform. While the static length scales accompanying this phenomenon do not seem to exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We further study quantum jamming and illustrate how a hard-core bosonic system can undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent z > 4 that is consistent with length scales that increase far more slowly than the relaxation time as a putative critical transition is approached. Similar results may hold for spin-liquid-type as well as interacting electronic systems. We suggest ways to analyze experimental data in order to adduce such phenomena. Our approach may be used to analyze other quenched quantum systems.
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