Finite-block approach to the ground-state energy of quantum spin systems

V. Ya. Krivnov, А. А. Овчинников

A new variational method for determining the ground-state energy of quasi-1D systems is proposed. The method consists of decomposition of a lattice into non-interacting blocks. A trial wavefunction is the product of exact ground-state block functions multiplied by operator correlation factors. The ground-state energy of a spin-1/2 and fermionic particle ladder is evaluated. The calculation is very simple and gives energies with an accuracy of about 2% or even less.

Eric R. Anschuetz, David Gamarnik, Bobak T. Kiani

Hiroshi Takizawa, Akihide Oguchi

Marie-Bernadette Lepetit, Efstratios Manousakis

We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.

Shuhua Li

The general formalism of the block-correlated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the ground-state electronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of many-electron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important many-electron state of each system block. By truncating the cluster operator to a certain n-block correlation level, an approximate but size-extensive BCCC method, denoted as BCCCn, is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of many-electron states for each block. I have implemented the BCCCn (n=2,3) methods within the S=1/2 Heisenberg Hamiltonian, and applied them to calculate the ground-state energies of one-dimensional spin chains and quasi-one-dimensional two-leg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory ground-state energies for these spin systems.

Masanori Ohya, Dėnes Petz