Simulations of quantum many-body problems via tensor network states

Abstract: The projected entangled pair states (PEPS) methods have been proved to be powerful tools to

solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high

computational scaling with the virtual bond dimension D, PEPS are often limited to rather small bond

dimensions. The optimization of the ground state using imaginary time evolution method with simple

update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation

to the environment of the local tensors is questionable.

 

We demonstrate that combining the Monte Carlo sampling techniques and gradient optimization offers

an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel

computing, we can study the quantum systems with larger bond dimensions up to D=16 without resorting

to any symmetry. We apply this method to J1-J2 model. Our results suggest that the ground state in the r

egion of J2 ~0.42 – 0.6 is a gapless spin liquid. We discuss the extension of this method to fermion systems.

 

个人简历:何力新教授1994年毕业于中国科技大学物理系, 并于1997年获中国科技大学硕士学位。 1998 - 2003年在美国

Rutgers 物理系师从 David Vanderbilt 教授学习第一性原理的计算方法,并获博士学位。2003.9-2006.1在美国国家再生能

源实验室Dr. Alex Zunger 领导的固体理论小组从事半导体量子点的理论研究工作。20061月作为国外杰出人才 (百人计

)引进至中国科技大学中科院量子信息重点实验室工作。 2010年获基金委杰出青年科学基金。2012年入选 IOP fellow

UK)。2011-2015任科技部量子调控量子通信网络和量子仿真关键器件的物理实现项目首席科学家。