Path-integral Monte Carlo

A Markov-chain Monte Carlo method for quantum many body systems. Simulation by this method is based on a Markov process in the space of d+1 dimensional configurations obtained via path-integral representation of d dimensional quantum many-body systems. The method is also called the world-line Monte Carlo. While the weight of a given state can be easily computed in classical systems, its computational cost for quantum systems is exponentially high. Therefore, the mapping into the d+1 dimensional classical problem through Suzuki-Trotter transformation or high-temperature series expansion is necessary for reducing the cost to a manageable level. The method is applied to various strongly-correlated lattice models such as transverse Ising model, Heisenberg model, and Hubbard model, as well as bosonic systems such as He4. However, in application to frustrated Heisenberg models and fermionic systems, the weight can be negative in general, making the method unpractical. This problem is called the negative sign problem, the most severe limitation of the method in studying quantum many-body systems.

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