Igor S. Tupitsyn

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model

We report a new type of multicritical point that arises from competition between the Higgs and confinement transitions in a Z2 gauge system. The phase diagram of the 3d gauge Higgs model has been obtained by Monte-Carlo simulation on large (up to 60) lattices. We find the transition lines continue as 2nd-order until merging into a 1st-order line. These findings pose the question of an effective field theory for a multicritical point involving noncommuting order parameters. A similar phase diagram is predicted for the 2-dimensional quantum toric code model with two external fields, hz and hx; this problem can be mapped onto an anisotropic 3D gauge Higgs model.

Coulomb and electron-phonon interactions in metals

An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this nonperturbative system were relying on uncontrolled approximations in the absence of small parameters. In this paper, we develop the diagrammatic Monte Carlo approach for a two-component Coulomb system that obtains the solution to this fundamental problem in an approximation-free way by computing vertex corrections from higher-order skeleton graphs. The feasibility of the method is demonstrated by calculating the spectrum of longitudinal acoustic phonons in a simple cubic lattice, determining their sound velocity, and obtaining the phonon spectral densities by analytic continuation of the Matsubara-Greens functions. Final results are checked against the lowest-order fully self-consistent

Wigner crystallization in the lowest Landau level for nu >= 1/5.

GW

Dielectric function and thermodynamic properties of jellium in the G W approximation

approximation in both adiabatic and nonadiabatic regimes.

Magnetic correlations in the two-dimensional repulsive Fermi Hubbard model

By means of exact diagonalization we study the low-energy states of seven electrons in the lowest Landau level which are confined by a cylindric external potential modelling the rest of a macroscopic system and thus controlling the filling factor

Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

\nu

Tunneling and inversion symmetry in single-molecule magnets: The case of the Mn12 wheel molecule

. Wigner crystal is found to be the ground state for filling factors between

Effective Hamiltonian in the Problem of a

\nu = 1/3