The Quantum Monte Carlo Diagonalization method for solving quantum many-body problems has been proposed, and its applications to the nuclear shell model have been extensively developed. This application is called Monte Carlo Shell Model. The actual numerical calculations of Monte Carlo Shell Model can be carried out very efficiently by a massive parallel computer, and indeed we have introduced one called Alphleet to RIKEN recently. A brief sketch of the Monte Carlo Shell Model and its parallel computing are presented.The Quantum Monte Carlo Diagonalization method for solving quantum many-body problems has been proposed, and its applications to the nuclear shell model have been extensively developed. This application is called Monte Carlo Shell Model. The actual numerical calculations of Monte Carlo Shell Model can be carried out very efficiently by a massive parallel computer, and indeed we have introduced one called Alphleet to RIKEN recently. A brief sketch of the Monte Carlo Shell Model and its parallel computing are presented.

Progress of Theoretical Physics SupplementJan 1, 20003 citations

A quantum Monte Carlo approach to many-body physics

Wolfgang von der Linden

Physics ReportsNov 1, 1992242 citations

Quantum Monte Carlo Method without Hubbard-Stratonovich Transformation for Many-body Systems

J. Wang, Weiwei Pan, D. Y. Sun

By precisely writing down the matrix element of the local Boltzmann operator ( $e^(-{\tau}h$ ), where h is the paired operator formed by two interacting terms conjugate to each other), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. Our formula presents remarkable outcomes such that: 1) the Hubbard-Stratonovich transformation is not necessary, and the auxiliary field is no longer needed, which can improve the computational efficiency. 2) The new formula improves the accuracy of the Suzuki-Trotter decomposition. Our method also provides a potential theoretical framework for analyzing and solving the fermion sign problem. As an example, we studied the one-dimensional half-filled Hubbard model at a finite temperature. The obtained results were in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be used in various studies.By precisely writing down the matrix element of the local Boltzmann operator ($e^(-{\tau}h$), where h is the paired operator formed by two interacting terms conjugate to each other), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. Our formula presents remarkable outcomes such that: 1) the Hubbard-Stratonovich transformation is not necessary, and the auxiliary field is no longer needed, which can improve the computational efficiency. 2) The new formula improves the accuracy of the Suzuki-Trotter decomposition. Our method also provides a potential theoretical framework for analyzing and solving the fermion sign problem. As an example, we studied the one-dimensional half-filled Hubbard model at a finite temperature. The obtained results were in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be used in various studies.

Oct 17, 20210 citations

By precisely writing down the matrix element of the local Boltzmann operator (

e^(-{\tau}h

), where h is the paired operator formed by two interacting terms conjugate to each other), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. Our formula presents remarkable outcomes such that: 1) the Hubbard-Stratonovich transformation is not necessary, and the auxiliary field is no longer needed, which can improve the computational efficiency. 2) The new formula improves the accuracy of the Suzuki-Trotter decomposition. Our method also provides a potential theoretical framework for analyzing and solving the fermion sign problem. As an example, we studied the one-dimensional half-filled Hubbard model at a finite temperature. The obtained results were in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be used in various studies.