  We present a tree-tensor-network-based method to study strongly correlated
systems with nonlocal interactions in higher dimensions. Although the
momentum-space and quantum-chemistry versions of the density matrix
renormalization group (DMRG) method have long been applied to such systems, the
spatial topology of DMRG-based methods allows efficient optimizations to be
carried out with respect to one spatial dimension only. Extending the
matrix-product-state picture, we formulate a more general approach by allowing
the local sites to be coupled to more than two neighboring auxiliary subspaces.
Following Shi. et. al. [Phys. Rev. A, 74, 022320 (2006)], we treat a tree-like
network ansatz with arbitrary coordination number z, where the z=2 case
corresponds to the one-dimensional scheme. For this ansatz, the long-range
correlation deviates from the mean-field value polynomially with distance, in
contrast to the matrix-product ansatz, which deviates exponentially. The
computational cost of the tree-tensor-network method is significantly smaller
than that of previous DMRG-based attempts, which renormalize several blocks
into a single block. In addition, we investigate the effect of unitary
transformations on the local basis states and present a method for optimizing
such transformations. For the 1-d interacting spinless fermion model, the
optimized transformation interpolates smoothly between real space and momentum
space. Calculations carried out on small quantum chemical systems support our
approach.
