118570813
Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas
We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. Our results compare favorably with exact numerical diagonalization results and with previous coordinate-space Monte Carlo calculations.
124451495
Lefschetz thimble Monte Carlo for many-body theories: A Hubbard model study
117551201
Quantum field theories on the Lefschetz thimble
In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.
67814332
An efficient method to compute the residual phase on a Lefschetz thimble
We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly with the number of stochastic estimators and quadratically with the length of the extra dimension along the gradient flow. This is a drastic improvement over previous estimates of the cost of computing the residual phase. We also report on basic tests of correctness and scaling of the code.
22141493
Odd-particle systems in the shell model Monte Carlo method: circumventing a sign problem.
The shell model Monte Carlo method is a powerful technique to calculate thermal and ground-state properties of strongly correlated finite-size systems. However, its application to odd-particle-number systems has been hampered by the sign problem that originates from the projection on an odd number of particles. We circumvent this sign problem for the ground-state energy by extracting the ground-state energy of the odd-particle-number system from the asymptotic behavior of the imaginary-time single-particle Green's function of the even-particle-number system. We apply this method to calculate pairing gaps of nuclei in the iron region. Our results are in good agreement with experimental pairing gaps.
118328762
Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem
We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to 8^4 using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that - at least in the case of the relativistic Bose gas - the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability - in principle - of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.
2554754
ON THE SIZE OF HADRONS
The form factor and the mean-square radius of the pion are calculated analytically from a parametrized form of a wave function. The numerical wave function was obtained previously by solving numerically an eigenvalue equation for the pion in a particular model. The analytical formulas are of more general interest than just being valid for the pion and can be generalized to the case with unequal quark masses. Two different parametrizations are investigated. Because of the highly relativistic problem, noticeable deviations from a nonrelativistic formula are obtained.
119189098
Chiral Odd Generalized Parton Distributions in Impact Parameter Space
We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. This provides a field theory inspired model of a relativistic spin-(1/2) composite state with the correct correlation between the different light-front wave functions (LFWFs) in Fock space. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.
55544629
Universality of TMD correlators
In a high-energy scattering process with hadrons in the initial state, color is involved. Transverse momentum dependent distribution functions (TMDs) describe the quark and gluon distributions in these hadrons in momentum space with the inclusion of transverse directions. Apart from the (anti)-quarks and gluons that are involved in the hard scattering process, additional gluon emissions by the hadrons have to be taken into account as well, giving rise to Wilson lines or gauge links. The TMDs involved are sensitive to the process under consideration and hence potentially nonuniversal due to these Wilson line interactions with the hard process; different hard processes give rise to different Wilson line structures. We will show that in practice only a finite number of universal TMDs have to be considered, which come in different linear combinations depending on the hard process under consideration, ensuring a generalized universality. For quarks this gives rise to three Pretzelocity functions, whereas for gluons a richer structure of functions arises.
120507485
A Study Of Generalized Parton Distributions In Position Space
Abstract We present a study of the parton distributions in transverse position or impact parameter space for the chiral odd GPDs of a dressed quark in QED. We also present an analysis of a recent parametrization for the chiral even GPDs inside a proton. We also discuss the region of validity of the parametrizations based on a positivity condition.
124138685
Jet Production in $pp$ Collisions: Dependence on Jet Algorithm