![]() Specifically, we investigate the U(1) and SU(2) symmetric ground state properties of next-nearest neighbor Hubbard model with next-nearest neighbor hopping amplitude t 2 = -0.25 at 1/8 hole doping. nearest-neighbor Heisenberg model) and an exactly solvable free-fermion model. We validate our iPEPS implementation using well-understood models (e.g. The quantum lattice models studied in this thesis include the Heisenberg model, the free-fermion model and the Hubbard model. This dramatically reduces the numerical costs and allows quantum states which conserve different types of symmetries can be studied. The QSpace tensor library is utilized to automatically keep track of the U(1) or SU(2) symmetry of the tensors. Therefore, it is particularly suitable for studying fermionic models such as the Hubbard model where numerous captivating phenomena including high-T c superconductivity may emerge.Ī unique feature of our iPEPS algorithms is the capability to exploit symmetries. Compared with other popular numerical methods such as the Density Matrix Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) method, iPEPS is especially competitive in its faithful representation of the entanglement area law and is free from the sign problem. In this thesis, we employ the infinite Projected Entangled-Pair State (iPEPS) tensor network to simulate 2-dimensional quantum models defined on a square lattice with nearest-neighbor and next-nearest neighbor interactions. Tensor network techniques provide a compelling framework to circumvent the complexity problem. However, direct treatment of a many-body system is close to impossible due to the exponentially large number of degrees of freedom. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.Various fascinating phenomena and phases of matter that emerge from the strongly correlated many-body systems have received much interest in condensed matter physics. The list of its authors can be seen in its historical and/or the page Edithistory:QSPACE.
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