Systematic speedup of path integrals of a generic N-fold discretized theory

@article{Bogojevic2005SystematicSO,
  title={Systematic speedup of path integrals of a generic N-fold discretized theory},
  author={Aleksandar Bogojevic and Antun Balaz and Aleksandar Belic},
  journal={Physical Review B},
  year={2005},
  volume={72},
  pages={064302}
}
We present and discuss a detailed derivation of an analytical method that systematically improves the convergence of path integrals of a generic N-fold discretized theory. We develop an explicit procedure for calculating a set of effective actions S{sup (p)}, for p=1,2,3,... which have the property that they lead to the same continuum amplitudes as the starting action, but converge to that continuum limit ever faster. Discretized amplitudes calculated using the p-level effective action differ… Expand
15 Citations

Figures from this paper

Fast convergence of path integrals for many-body systems
Abstract We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developingExpand
Fast Converging Path Integrals for Time-Dependent Potentials
We calculate the short-time expansion of the propagator for a general many-body quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end theExpand
Energy estimators and calculation of energy expectation values in the path integral formalism
Abstract A recently developed method systematically improved the convergence of generic path integrals for transition amplitudes [A. Bogojevic, A. Balaž, A. Belic, Phys. Rev. Lett. 94 (2005) 180403,Expand
Properties of quantum systems via diagonalization of transition amplitudes. I. Discretization effects.
TLDR
It is shown that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with 1/Delta(2), which is particularly well suited for numerical studies of few-body quantum systems. Expand
SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach
We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-timeExpand
Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization forExpand
Ultra-fast converging path-integral approach for rotating ideal Bose–Einstein condensates
A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numericallyExpand
Energy levels and expectation values via accelerated path integral Monte Carlo
A recently developed method systematically improved the convergence of generic path integrals for transition amplitudes, partition functions, expectation values and energy spectra. This was achievedExpand
Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation.
TLDR
This paper applies recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. Expand
Efficient calculation of energy spectra using path integrals
Abstract A newly developed method for systematically improving the convergence of path integrals for transition amplitudes [A. Bogojevic, A. Balaž, A. Belic, Phys. Rev. Lett. 94 (2005) 180403, A.Expand
...
1
2
...

References

SHOWING 1-10 OF 20 REFERENCES
Systematically accelerated convergence of path integrals.
We present a new analytical method that systematically improves the convergence of path integrals of a generic N-fold discretized theory. Using it we calculate the effective actions S(p) for p< orExpand
Improved Feynman propagators on a grid and non-adiabatic corrections within the path integral framework
Abstract The idea of using a good representation as the zeroth order description of a problem, which is widely used in perturbation theory and in basis set calculations, is extended to the pathExpand
On the approximation of Feynman-Kac path integrals for quantum statistical mechanics
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a RiemannExpand
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections versus an effective propagator approach
Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method,Expand
Path integrals in the theory of condensed helium
One of Feynman`s early applications of path integrals was to superfluid {sup 4}He. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type ofExpand
Exponential power series expansion for the quantum time evolution operator
The coordinate matrix element of the time evolution operator, exp[−iHt/ℏ], is determined by expanding (its exponent) in a power series in t. Recursion relations are obtained for the expansionExpand
A quantum‐statistical Monte Carlo method; path integrals with boundary conditions
A new Monte Carlo method for problems in quantum‐statistical mechanics is described. The method is based on the use of iterated short‐time Green’s functions, for which ’’image’’ approximations areExpand
Applications of higher order composite factorization schemes in imaginary time path integral simulations
Suzuki’s higher order composite factorization which involves both the potential and the force is applied to imaginary time path integral simulation. The expression is more general than the originalExpand
Correct short time propagator for Feynman path integration by power series expansion in Δt
Abstract The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated “improved” ones) is not correct through first order in the timeExpand
Quark action for very coarse lattices
We investigate a tree-level O(a{sup 3})-accurate action, D234c, on coarse lattices. For the improvement terms we use tadpole-improved coefficients, with the tadpole contribution measured by the meanExpand
...
1
2
...