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Speaker: Mingpu Qin (School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China)
Combination of Tensor Network States and Green’s function Monte Carlo
We propose an approach to study the ground state of quantum many-body systems in which tensor network
states, specifically projected entangled pair states (PEPSs), and Green’s function Monte Carlo (GFMC) are
combined. PEPSs, by design, encode the area law which governs the scaling of entanglement entropy in quantum systems with short-range interactions but are hindered by the high computational complexity scaling with bond dimension D. GFMC is a highly efficient method, but it usually suffers from the infamous negative sign problem which can be avoided by the fixed-node approximation in which a guiding wave function is utilized to modify the sampling process. The trade-off for the absence of the negative sign problem is the introduction of systematic error by the guiding wave function. In this work, we combine these two methods, PEPS and GFMC, to take advantage of both of them. PEPSs are very accurate variational wave functions, while at the same time, only contractions of the single-layer tensor network are necessary in GFMC, which reduces the cost substantially. Moreover, energy obtained in GFMC is guaranteed to be variational and lower than the variational energy of the guiding PEPS wave function. Benchmark results of the J1-J2 Heisenberg model on the square lattice are provided.