Related papers: Approximate two-body generating Hamiltonian for th…
The PH-Pfaffian state having 1/2 central charge is consistent with the thermal Hall conductance measurement of 5/2 fractional quantum Hall system, but lacks support from the existing numerical results. In this paper we propose a new state…
We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (`PH-Pfaffian') topological order, a phase consistent with the recently reported thermal Hall conductance [Banerjee et al., Nature 559,…
We derive one-dimensional effective Hamiltonians for spin-orbit coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For energy regime around the two-body bound state energy, the effective Hamiltonian takes a…
In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL}…
It is shown for two electron atoms that ground-state wavefunctions of the form \begin{equation} \Psi(\vec{r_{1}}, \vec{r_{2}})=\phi(\vec{r_{1}})\phi(\vec{r_{2}})(\cosh ar_{1}+\cosh ar_{2})(1+0.5 r_{12}e^{-b r_{12}}) \end{equation} where…
A recent thermal Hall conductance experiment [Banerjee et al., Nature {\bf559}, 205 (2018)] for $\nu = 5/2$ fractional quantum Hall system appears to rule out both the Pfaffian and anti-Pfaffian and be in favor of the PH-Pfaffian…
We consider a two dimensional (2D) model of particles interacting in a Landau level. We work in a finite disk geometry and take the particles to interact with a linearly decreasing two-body Haldane pseudo-potential. We show that the ground…
We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians…
We propose a derivative operator formed as a function of derivatives of the electron coordinates. When the derivative operator is applied to the Laughlin wave function, two new wave functions in the lowest Landau level at filling factor 1/2…
We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and…
We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at…
There is much interest in the realization of systems with p-wave pairing in one dimension or chiral p-wave pairing in two dimensions, because these are believed to support Majorana modes at the ends or inside vortices. We consider a two…
The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions,…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
An analytical approximation for the eigenvalues of $\mathcal{PT}$ symmetric Hamiltonian $\mathsf{H} = -d^{2}/dx^{2} - (\mathrm{i}x)^{\epsilon+2}$, $\epsilon > -1$ is developed via simple basis sets of harmonic-oscillator wave functions with…
The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This…
We derive the exact form of the bosonized Hamiltonian for a many-body fermion system in one spatial dimension with arbitrary dispersion relations, using the droplet bosonization method. For a single-particle Hamiltonian polynomial in the…
We construct many particle Hamiltonians for which the Laughlin and Jain wavefunctions are exact ground states. The Hamiltonians involve fermions in a magnetic field and with inter-particle interactions. For the Laughlin wave-functions,the…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…