DMRG Study Of 2d Frustrated Spin Systems And Tensor Product State Method

An important challenge in condensed matter physics is the search for the quan-tum disordered ground states in two-dimensional (2D) systems. Of particular interestis studying the quantum spin liquids, which most likely exist in the frustrated spin sys-tems. In the first part of this paper, we will use density matrix renormalization group(DMRG) method to systematically study the ground state properties of several 2D frus-trated quantum systems. (a) For the spin-1/2 kagome antiferromagnet, we find that theground state is a magnetically disordered spin liquid state, without long-range mag-netic order, with a finite spin triplet excitation gap and gapless singlet excitations. (b)For the spin-1/2 antiferromagnetic XXZ model on the triangular lattice (i.e. frustratedhard-core boson at half-filling), we get the ground state phase diagram and identify arobust supersolid phase, surviving in the Ising limit. (c) For the spatially anisotropicspin-1 J1?J2 model on the square lattice, we obtain the ground state phase diagram andidentify the existence of an intermediate quantum paramagnetic region for all values ofthe anisotropy, separating the Neel phase and stripe phase.The second part is about the tensor product state (TPS) method. In this part, wewill introduce our recent works by developing a novel projection method, which allowsa TPS wave function to be handled accurately and e?ciently in the thermodynamiclimit. We also propose a novel second renormalization group (SRG) method to handlethe tensor-network states or models. This method reduces dramatically the truncationerror of the tensor renormalization group (TRG). It allows physical quantities of clas-sical tensor product models or tensor product ground states of quantum systems to beaccurately and e?ciently determined. These two methods have potential to become avery powerful numerical tool in the future to investigate 2D strongly correlated electronsystems.