We propose a method for calculating the excited-state properties of a quantum many-fermion system based on the auxiliary-field Monte-Carlo method. We have examined our method with the exactly solvable pairing-force model and the Lipkin model.
Quantum Monte Carlo simulations provide a powerful tool to compute static properties of quantum many-particles models and realistic systems. A vast array of ground-state energies and properties defined by equal-time correlation functions can be computed with high accuracy. On the other hand, the extensions needed to study time-displaced correlation functions, which provide access to excited states, have been challenging, especially for fermionic strongly correlated systems. The authors present a methodology that allows a high-accuracy calculation of the dynamical Green functions of many-fermions systems in the framework of the auxiliary-field quantum Monte Carlo method. They extract the the charge gap of the repulsive two-dimensional Hubbard model at half-filling as a function of the interaction strength and propose strategies for applying their methodology to more realistic systems.
Quantum Monte Carlo simulations provide a powerful tool to compute static properties of quantum many-particle models and realistic systems. Here, the authors present a technique to reduce the computational cost of computing ground-state energies, properties, and correlation functions in the framework of the auxiliary-field quantum Monte Carlo method. This is based on a simple application of group theory, and can be readily transferred to other computational methodologies for many-particle systems.
We solve the zero-temperature unitary Fermi gas problem by incorporating a BCS importance function into the auxiliary-field quantum Monte Carlo method. We demonstrate that this method does not suffer from a sign problem and that it increases the efficiency of standard techniques by many orders of magnitude for strongly paired fermions. We calculate the ground-state energies exactly for unpolarized systems with up to 66 particles on lattices of up to 273 sites, obtaining an accurate result for the universal parameter $\ensuremath{\xi}$. We also obtain results for interactions with different effective ranges and find that the energy is consistent with a universal linear dependence on the product of the Fermi momentum and the effective range. This method will have many applications in superfluid cold atom systems and in both electronic and nuclear structures where pairing is important.
A new Monte Carlo method for computing excited state properties of quantum systems is introduced. It is a generalization of the transient estimate method used for fermion Green’s function Monte Carlo and of subspace projection methods used for computing eigenstates of matrices. The time dependent autocorrelation function of a vector of trial functions is calculated for a random walk generated by the imaginary-time Schrödinger equation and estimates of energy levels are determined by the eigenvalues of the matrix of correlation functions. This method is especially useful for treating states with the same symmetry as it automatically keeps higher states orthogonal to lower states. The estimated energy converges to the exact eigenvalue with a rate which decreases with increasing excitation energy, thus limiting the method to relatively low-lying states. The method is zero variance in the sense that as better trial functions are introduced, the statistical error decreases to zero. The method has a nontrivial bias which is analyzed. As an illustration, the eigenvalues of a double well are computed.