Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory

Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is difficult to realize in experiments. It seems, however, that such long-range interactions should not be necessary, as the correlations decay exponentially in the bulk. This poses the question, whether the Hamiltonians can be truncated to contain only local interactions without changing the physics of the ground state. Previous studies have in a couple of cases with particularly much symmetry obtained such local Hamiltonians by keeping only a few local terms and numerically optimizing the coefficients. Here, we investigate a different strategy to construct truncated Hamiltonians, which does not rely on optimization, and which can be applied independent of the choice of lattice. We test the approach on two models with bosonic Laughlin-like ground states with filling factor $1/2$ and $1/4$, respectively. We first investigate how the coupling strengths in the exact Hamiltonians depend on distance, and then we study the truncated models. For the case of $1/2$ filling, we find that the truncated model with truncation radius $\sqrt{2}$ lattice constants on the square lattice and $1$ lattice constant on the triangular lattice has an approximate twofold ground state degeneracy on the torus, and the overlap per site between these states and the states constructed from conformal field theory is higher than $0.99$ for the lattices considered. For the model at $1/4$ filling, our results give some hints that a truncation radius of $\sqrt{5}$ on the square lattice and $\sqrt{7}$ on the triangular lattice might be enough, but the finite size effects are too large to judge whether the topology is, indeed, present in the thermodynamic limit.Comment: 8 Pages, 10 Figure

Sudden quench of harmonically trapped mass-imbalanced fermions

© 2022, The Author(s).Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system’s evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.11Nsciescopu

Relativistic-coupled-cluster-theory analysis of properties of Co-like ions

Ionization potentials, excitation energies, transition properties, and hyperfine structure constants of the low-lying 3p63d9 2D5/2, 3p63d9 2D3/2, 3p53d10 2P3/2, and 3p53d10 2P1/2 atomic states of the Co-like highly charged ions such as Y12+, Zr13+, Nb14+, Mo15+, Tc16+, Ru17+, Rh18+, Pd19+, Ag20+, and Cd21+ are investigated. The singles and doubles approximated relativistic coupled-cluster theory in the framework of one electron removal Fock-space formalism is employed over the Dirac-Hartree-Fock calculations to account for the electron correlation effects for determining the aforementioned properties. Higher-order relativistic corrections due to the Breit interaction and quantum electrodynamics effects in the evaluation of energies are also quantified explicitly. Our estimated values are compared with the other available theoretical calculations and experimental results, which are found to be in good agreement with each other.11Nsciescopu

Forbidden transition properties in the ground-state configurations of singly ionized noble gas atoms for stellar and interstellar media

High-accuracy calculations of the forbidden transition amplitudes for the np 2P1/2 → np 2P3/2 transitions with the ground-state principal quantum number n in singly charged inert gas atoms, which are of astrophysical interest, have been carried out using sophisticated relativistic many-body methods. Using these amplitudes, the line strengths, oscillator strengths and transition probabilities of the above transitions and lifetimes of the np 2P1/2 states are estimated precisely. Most of these transition wavelengths lie in the infrared region, while the corresponding Rn ii line is the optical one, and they can be observed in the stellar and interstellar media, where the abundances of these ions have already been identified. The above forbidden transitions can also be very useful for astrophysical plasma diagnostics and can guide experiments to measure the lifetimes of the above np 2P1/2 states.by D.K. Nandy and B.K. Saho

Relativistic calculations of radiative properties and fine structure constant varying sensitivity coefficients in the astrophysically relevant Zn II, Si IV and Ti IV ions

We have carried out calculations of the relativistic sensitivity coefficients, oscillator strengths, transition probabilities, lifetimes and magnetic dipole hyperfine structure constants for a number of low-lying states in the Zn ii, Si iv and Ti iv ions which are abundant in the distant quasars and various stellar plasmas. These spectroscopic data will be very useful for probing temporal variation of the fine structure constant (αe) and in the diagnostic processes of some of the astrophysical plasmas. We have employed all-order perturbative methods in the relativistic coupled-cluster framework using the Dirac–Coulomb Hamiltonian to calculate the atomic wavefunctions of the considered ions. Reference states are constructed with the VN−1 and VN+1 potentials and then the electron–electron correlation effects are taken into account by constructing all possible singly and doubly excited configurations, involving both the core and valence electrons, from the respective reference states. We have also determined one electron affinities and ionization potentials of many excited states in these Zn ii, Si iv and Ti iv ions. Except for a few states we have attained accuracies within 1 per cent for the energies compared with their experimental values. Our calculated sensitivity coefficients are estimated to have similar accuracies as of the calculated energies. Furthermore, combining our calculated transition matrix elements with the experimental wavelengths we evaluate transition probabilities, oscillator strengths and lifetimes of some of the excited states in these ions. These results are compared with the available data in a few cases and found to be in very good agreement among themselves. Using our reported hyperfine structure constants due to the dominant magnetic dipole interaction, it is possible to determine hyperfine splittings approximately in the above considered ions.by D.K. Nandy and B.K Saho

Quadrupole shifts for the Yb + 171 ion clocks: Experiments versus theories

[4f146s]2S1/2→[4f145d]2D3/2,[4f146s]2S1/2→[4f145d]2D5/2, and [4f146s]2S1/2→[4f136s2]2F7/2, in the Yb+ ion are investigated by calculating values of the quadrupole moment (Θ) for the 5d3/2,5/2 and 4f7/2 states using the relativistic coupled-cluster (RCC) methods. We find an order of magnitude difference in the Θ value of the 4f7/2 state between our calculation and the experimental result, but our result concurs with that of other calculations carried out using many-body methods different from ours. However, our Θ value of the 5d3/2 state is in good agreement with the available experimental result and is highly precise. This enables us to estimate the quadrupole shift of the [4f146s]2S1/2→[4f145d]2D3/2 clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the 6s1/2,5d3/2,5/2, and 4f7/2,5/2 states of the Yb+171 ion using the same RCC methods and compare the results with the experimental values. We also determine the lifetime of the 5d3/2 state to address a discrepancy between conflicting values given by recent experiments.D.K. Nandy and B.K. Saho

Quadrupole shifts for the 171Yb+ ion clocks: experiments versus theories

Quadrupole shifts for three prominent clock transitions, [4f146s]2S1/2→[4f145d]2D3/2, [4f146s]2S1/2→[4f145d]2D5/2 and [4f146s]2S1/2→[4f136s2]2F7/2, in the Yb+ ion are investigated by calculating quadrupole moments (Θs) of the 5d3/2,5/2 and 4f7/2 states using the relativistic coupled-cluster (RCC) methods. We find an order difference in the Θ value of the 4f7/2 state between our calculation and the experimental result, but our result concur with the other calculations that are carried out using different many-body methods than ours. Nevertheless, our Θ value of the 5d3/2 state is in good agreement with the available experimental result and becomes more precise till date estimating the quadrupole shift of the [4f146s]2S1/2→[4f145d]2D3/2 clock transition more accurately. To justify accuracies in our calculations, we also evaluate the hyperfine structure constants of the 6s1/2, 5d3/2,5/2 and 4f7/2,5/2 states of 171Yb+ ion using the same RCC method and compare the results with their experimental values. Moreover, we determine lifetime of the 5d3/2 state to eradicate disagreement on its value from two different experiments

Few-particle dynamics of fractional quantum Hall lattice models Phys. Rev. B 101, 205305 – Published 15 May 2020

Considering lattice Hamiltonians designed using conformal field theory to have fractional quantum Hall states as ground states, we study the dynamics of one or two particles on such lattices. Examining the eigenspectrum and dynamics of the single-particle sector, we demonstrate that these Hamiltonians cannot be regarded as describing interacting particles placed on a Chern band, so that the physics is fundamentally different from fractional Chern insulators. The single-particle spectrum is shown to consist of eigenstates localized in shells which have a larger radius for larger eigenenergies. This leads to chiral dynamics along reasonably well-defined orbits, in both the single-particle and the two-particle sectors