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1. Integrability of the ν=4/3 fractional quantum Hall edge states

   https://doi.org/10.22331/q-2022-06-14-736  

   Hu, Yichen ; Lian, Biao ( June 2022 , Quantum)

   We investigate the homogeneous chiral edge theory of the filling ν = 4 / 3 fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge 2 e 3 chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each conserved charge and momentum sector, indicating the existence of hidden conserved quantities and the possibility that the generic edge theory of the ν = 4 / 3 fractional quantum Hall state is integrable. We further show that a global symmetry preserving irrelevant nonlinear kinetic term will lead to the transition of LSS from Poisson to Wigner-Dyson at high energies. This further supports the possibility that the model without irrelevant terms is integrable. 

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2. Engineering parafermions in helical Luttinger liquids

   https://doi.org/10.1117/12.2595632  

   Lyanda-Geller, Yuli ; Ponomarenko, Vadim ; Wang, Ying ; Rokhinson, Leonid ( August 2021 , SPIE Nanoscience + Engineering)

   Drouhin, Henri-Jean M. ; Wegrowe, Jean-Eric ; Razeghi, Manijeh (Ed.)

   Parafermions or Fibonacci anyons leading to universal quantum computing, require strongly interacting systems. A leading contender is the fractional quantum Hall effect, where helical channels can arise from counterpropagating chiral modes. These modes have been considered weakly interacting. However, experiments on transport in helical channels in the fractional quantum Hall effect at a 2/3 filling shows current passing through helical channels on the boundary between polarized and unpolarized quantum Hall liquids nine-fold smaller than expected. This current can increase three-fold when nuclei near the boundary are spin polarized. We develop a microscopic theory of strongly interacting helical states and show that emerging helical Luttinger liquid manifests itself as unequally populated charge, spin and neutral modes in polarized and unpolarized fractional quantum Hall liquids. We show that at strong coupling counter-propagating modes of opposite spin polarization emerge at the sample edges, providing a viable path for generating proximity topological superconductivity and parafermions. Current, calculated in strongly interacting picture is in agreement with the experimental data. 

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3. The Teleparallel Equivalent of Newton-Cartan Gravity

   Teh, N. ; Read, J. ( August 2018 , Classical and quantum gravity)

   We construct a notion of teleparallelization for Newton–Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton–Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity. 

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4. Room temperature electrically pumped topological insulator lasers

   https://doi.org/10.1038/s41467-021-23718-4  

   Choi, Jae-Hyuck ; Hayenga, William E. ; Liu, Yuzhou G. ; Parto, Midya ; Bahari, Babak ; Christodoulides, Demetrios N. ; Khajavikhan, Mercedeh ( December 2021 , Nature Communications)

   null (Ed.)

   Abstract Topological insulator lasers (TILs) are a recently introduced family of lasing arrays in which phase locking is achieved through synthetic gauge fields. These single frequency light source arrays operate in the spatially extended edge modes of topologically non-trivial optical lattices. Because of the inherent robustness of topological modes against perturbations and defects, such topological insulator lasers tend to demonstrate higher slope efficiencies as compared to their topologically trivial counterparts. So far, magnetic and non-magnetic optically pumped topological laser arrays as well as electrically pumped TILs that are operating at cryogenic temperatures have been demonstrated. Here we present the first room temperature and electrically pumped topological insulator laser. This laser array, using a structure that mimics the quantum spin Hall effect for photons, generates light at telecom wavelengths and exhibits single frequency emission. Our work is expected to lead to further developments in laser science and technology, while opening up new possibilities in topological photonics. 

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5. A Charged Particle with Anisotropic Mass in a Perpendicular Magnetic Field–Landau Gauge

   https://doi.org/10.3390/sym16040414  

   Ciftja, Orion ( April 2024 , Symmetry)

   The loss of any symmetry in a system leads to quantum problems that are typically very difficult to solve. Such a situation arises for particles with anisotropic mass, like electrons in various semiconductor host materials, where it is known that they may have an anisotropic effective mass. In this work, we consider the quantum problem of a spinless charged particle with anisotropic mass in two dimensions and study the resulting energy and eigenstate spectrum in a uniform constant perpendicular magnetic field when a Landau gauge is adopted. The exact analytic solution to the problem is obtained for arbitrary values of the anisotropic mass using a mathematical technique that relies on the scaling of the original coordinates. The characteristic features of the energy spectrum and corresponding eigenstate wave functions are analyzed. The results of this study are expected to be of interest to quantum Hall effect theory.

    

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