33 research outputs found
Density matrix renormalization group study of optical conductivity in the one-dimensional Mott insulator Sr_2CuO_3
Applying newly developed dynamical density matrix renormalization group
techniques at zero and finite temperatures to a Hubbard-Holstein model at
half-filling, we examine the optical conductivity of a typical one-dimensional
Mott insulator Sr_2CuO_3. We find a set of parameters in the Hubbard-Holstein
model, which can describe optical conductivity for both Mott-gap excitation in
the high-energy region and phonon-assisted spin excitation in the low-energy
region. We also find that electron-phonon interaction gives additional
broadening in the temperature dependence of the Mott-gap excitation.Comment: 5 pages, 3figure
Low-temperature density matrix renormalization group using regulated polynomial expansion
We propose a density matrix renormalization group (DMRG) technique at finite
temperatures. As is the case of the ground state DMRG, we use a single-target
state that is calculated by making use of a regulated polynomial expansion.
Both static and dynamical quantities are obtained after a random-sampling and
averaging procedure. We apply this technique to the one-dimensional Hubbard
model at half filling and find that this gives excellent results at low
temperatures.Comment: 5 pages, 3 figures. Accepted for publication in Phys. Rev.
Quantum annealing for systems of polynomial equations
Numerous scientific and engineering applications require numerically solving
systems of equations. Classically solving a general set of polynomial equations
requires iterative solvers, while linear equations may be solved either by
direct matrix inversion or iteratively with judicious preconditioning. However,
the convergence of iterative algorithms is highly variable and depends, in
part, on the condition number. We present a direct method for solving general
systems of polynomial equations based on quantum annealing, and we validate
this method using a system of second-order polynomial equations solved on a
commercially available quantum annealer. We then demonstrate applications for
linear regression, and discuss in more detail the scaling behavior for general
systems of linear equations with respect to problem size, condition number, and
search precision. Finally, we define an iterative annealing process and
demonstrate its efficacy in solving a linear system to a tolerance of
.Comment: 11 pages, 4 figures. Added example for a system of quadratic
equations. Supporting code is available at
https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review,
pre-copyedit version of an article published in Scientific Reports. The final
authenticated version is available online at:
https://www.nature.com/articles/s41598-019-46729-