arXiv subjects

Tim Byrnes

Publications and source records attributed to Tim Byrnes.

130 records · Page 8Linked to original sources

arXiv2007

Quantum simulation of Fermi-Hubbard models in semiconductor quantum dot arrays

We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of quantum dots defined in a semiconductor two-dimensional electron gas system. Bands with energies above the lowest energy band are used to form the Hubbard model, which allows for an experimentally simpler realization of the device. We find that depending on average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a d-wave superconducting phase should be observable using current fabrication technologies.

quant-ph↗

arXiv2006

Quantum simulator for the Hubbard model with long-range Coulomb interactions using surface acoustic waves

A practical experimental scheme for a quantum simulator of strongly correlated electrons is proposed. Our scheme employs electrons confined in a two dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface acoustic waves are then induced in the GaAs substrate, which create a two dimensional ``egg-carton'' potential. The dynamics of the electrons in this potential is described by a Hubbard model with long-range Coulomb interactions. The state of the electrons in this system can be probed via its conductance and noise properties. This allows the identification of a metallic or insulating state. Numerical estimates for the parameters appearing in the effective Hubbard model are calculated using the proposed experimental system. These calculations suggest that observations of quantum phase transition phenomena of the electrons in the potential array are within experimental reach.

cond-mat.str-el↗

arXiv2005

Simulating lattice gauge theories on a quantum computer

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.

quant-ph↗

arXiv2003

Renormalization of Anisotropy and Glueball Masses on Tadpole Improved Lattice Gauge Action

The Numerical calculations for tadpole-improved U(1) lattice gauge theory in three-dimensions on anisotropic lattices have been performed using standard path integral Monte Carlo techniques. Using average plaquette tadpole renormalization scheme, simulations were done with temporal lattice spacings much smaller than the spatial ones and results were obtained for the string tension, the renormalized anisotropy and scalar glueball masses. We find, by comparing the `regular' and `sideways' potentials, that tadpole improvement results in very little renormalization of the bare anisotropy and reduces the discretization errors in the static quark potential and in the glueball masses.

hep-lat↗