Quantum Monte Carlo diagonalization for many-fermion systems

Abstract

In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields, we expand the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis wave functions. The Hamiltonian is diagonalized to obtain the lowest energy state, using the variational principle within the selected subspace of the basis functions. This method is free from the difficulty known as the negative sign problem. We can optimize a wave function using two procedures. The first procedure is to increase the number of basis functions. The second improves each basis function through the operators, $e^{-\Delta \tau H}$, using the Hubbard-Stratonovich decomposition. We present an algorithm for the Quantum Monte Carlo diagonalization method using a genetic algorithm and the renormalization method. We compute the ground-state energy and correlation functions of small clusters to compare with available data.

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• Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems
• Time-dependent Gutzwiller theory of pairing fluctuations in the Hubbard model
• Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III --
• Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach
• Enhancement of superconductivity due to kinetic-energy effect in the strongly correlated phase of the two-dimensional Hubbard model
• Analytical Continuation Approaches to Electronic Transport: The Resonant Level Model
• Superconductivity and inhomogeneous charge-ordered state in the two-Dimensional Hubbard model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV