Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators
arXiv:2303.10301 · doi:10.1103/PhysRevB.107.235124
Abstract
We propose a new scheme to implement the self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo (CP-AFQMC) in the framewok of natural orbitals. In this scheme, a new trial wave-function in the form of Slater determinant is constructed from the CP-AFQMC results by diagonalizing the mixed estimator of the one-body reduced density matrix. We compare two ways (from real and mixed estimators in CP-AFQMC) to calculate the one-body reduced density matrix in the self-consistent process and study the ground state of doped two dimensional Hubbard model to test the accuracy of the two schemes. By comparing the local density, occupancy, and ground state energy we find the scheme in which one-body reduced density matrix is calculated from mixed estimator is computational more efficient and provides more accurate result with less fluctuation. The local densities from mixed estimator scheme agree well with the numerically exact values. This scheme provides a useful tool for the study of strongly correlated electron systems.
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References in corpus (19)
- Correlated Electrons in High Temperature Superconductors
- Continuous-time Monte Carlo methods for quantum impurity models
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Stripe order in the underdoped region of the two-dimensional Hubbard model
- The Hubbard Model
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- A Constrained Path Monte Carlo Method for Fermion Ground States
- Neel order in square and triangular lattice Heisenberg models
- Absence of superconductivity in the pure two-dimensional Hubbard model
- Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
- Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
- Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations
- Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
- Quantum Monte Carlo method for the ground state of many-boson systems
- Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
- Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures
- Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
- Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
- A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo