Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDiffusion in the Continuous-Imaginary-Time Quantum World-Line Monte Carlo Simulations with Extended Ensembles
194
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The dynamics of samples in the continuous-imaginary-time quantum world-line Monte Carlo simulations with extended ensembles are investigated. In the case of a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadratic model, the asymmetric behavior of Monte Carlo samples appears in the diffusion process in the space of the number of vertices. We prove that a local diffusivity is asymptotically proportional to the number of vertices, and we demonstrate the asymmetric behavior in the flat ensemble case. On the basis of the asymptotic form, we propose the weight of an optimal ensemble as $1/sqrt{n}$, where $n$ denotes the number of vertices in a sample. It is shown that the asymmetric behavior completely vanishes in the case of the proposed ensemble on the one-dimensional quantum S=1 bi-quadratic model.
rate research
Read More
In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as $1/Delta^2$, where $Delta$ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests there is no quantum advantage in using QAs w.r.t. quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model, where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving the door open for potential quantum speedup, even for stoquastic models. In this work, we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/Delta$, i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain points at an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the negative sign problem when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.
We present the global phase diagram of the extended boson Hubbard model on a simple cubic lattice by quantum Monte Carlo simulation with worm update algorithm. Four kinds of phases are supported by this model, including superfluid, supersolid, Mott, and charge density wave (CDW) states, which are identified in the phase diagram of chemical potential $mu$ versus nearest neighbor interaction V . By changing the chemical potential, a continuous transition is found from the Mott phase to a superfluid phase without breaking the translational symmetry. For an insulating CDW state, adding particles to it gives rise to a continuous transition to a supersolid phase, while removing particles usually leads to a first-order one to either supersolid or superfluid phase. By tuning the nearest neighbor interaction, one can realize the transition between two insulating phases, Mott and CDW with the same particle density, which turns out to be of the first-order. We also demonstrate that a supersolid phase with average particle density less than 1/2 can exist in a small region of $mu$ - V phase diagram.
We present Quantum Monte Carlo simulations of a generalization of the Feynman-Kikuchi model which includes the possibility of vacancies and interactions between the particles undergoing exchange. By measuring the winding number (superfluid density) and density structure factor, we determine the phase diagram, and show that it exhibits regions which possess both superfluid and charge ordering.
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
