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We show an implementation of density matrix embedding theory (DMET) for the spin lattice of infinite size. It is indeed a special form of hierarchical mean-field (HMF) theory. In the method, we divide the lattice into a small part and a large part. View the small part as an impurity, embedding in the large part, which is viewed as the environment. We deal the impurity with a high accuracy method. But treat the environment with a low-level method: the states of the environment nearby the impurity are expressed by a set of multiple block product states, while the distant parts are treated by mean-field consideration. Our method allows for the computation of the ground state of the infinite two-dimensional quantum spin systems. In the text, we take the frustrated Heisenberg model as an example to test our method. The ground state energy we calculated can reach a high accuracy. We also calculate the magnetization, and the fidelity to study the quantum phase transitions. [ABSTRACT FROM AUTHOR]

We use cluster density matrix embedding theory (CDMET) to calculate the excited states for quantum spin systems. The bath states are a set of block-product states and optimized by the variational method. By considering the symmetry in the form of penalty function, the degeneracy of excited eigenstates can be reduced. We prove the accuracy of our method by obtaining different excited states of square Heisenberg model. The ground state is nondegenerate state with gapless excitation in the ordered phase or degenerate state with an excitation energy gap in disordered phase. This is consistent with some previous results and supports the Lieb–Schultz–Mattis theorem. Moreover, we find some interesting behaviors of excited states for different coupling coefficient and different target energy under different symmetries. [ABSTRACT FROM AUTHOR]