Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models
arXiv:2006.02762 · doi:10.1140/epjb/s10051-021-00050-w
Abstract
We study the quantum self-organization of interacting particles in one-dimensional(1D) many-body systems, modeled via Hubbard chains with short-range interactions between the particles. We show the emergence of 1D states with density-wave and clustering order, related to topology, at odd denominator fillings that appear also in the fractional-quantum-Hall-effect (FQHE), which is a 2D electronic system with Coulomb interactions between the electrons and a perpendicular magnetic field. For our analysis we use an effective topological measure applied on the real space wavefunction of the system, the Euler characteristic describing the clustering of the interacting particles. The source of the observed effect is the spatial constraints imposed by the interaction between the particles. In overall, we demonstrate a simple mechanism to reproduce many of the effects appearing in the FQHE, without requiring a Coulomb interaction between the particles or the application of an external magnetic field.
arXiv comment6 pages, 5 figures, small updates in the text and the references, published in EPJ B
References in corpus (23)
- Quantum entanglement
- Fault-tolerant quantum computation by anyons
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Entanglement spectrum of a topological phase in one dimension
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Entanglement spectrum in one-dimensional systems
- Geometrical Description of the Fractional Quantum Hall Effect
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Experimental studies of the fractional quantum Hall effect in the first excited Landau level
- Entanglement entropy of excited states
- Quantum Hall system in Tao-Thouless limit
- Entanglement spectrum of the two dimensional Bose-Hubbard model
- Fractional topological phase in one-dimensional flatbands with nontrivial topology
- A graph theoretical Gauss-Bonnet-Chern Theorem
- Superfluid to Mott-insulator transition of hardcore bosons in a superlattice
- A study of cooperative breathing-mode in molecular chains
- An analysis of the model
- Exact results for the entanglement in 1D Hubbard models with spatial constraints
- Topological self-organization of strongly interacting particles
- Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints
- Self-organization in many-body systems with short-range interactions: clustering, correlations and topology