High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it XXZ} model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half {\it XXZ} model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUB$m$ scheme in which we retain all $k$-body correlations defined on all possible locales of $m$ adjacent lattice sites ($k \le m$). The ``raw'' CCM LSUB$m$ results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUB$m$ results to the limit $m \to \infty$ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground- and excited-state properties of these systems across a wide range of values of the anisotropy parameter.Comment: 31 Pages, 5 Figure

Quantum Phase Transitions in Spin Systems

We discuss the influence of strong quantum fluctuations on zero-temperature phase transitions in a two-dimensional spin-half Heisenberg system. Using a high-order coupled cluster treatment, we study competition of magnetic bonds with and without frustration. We find that the coupled cluster treatment is able to describe the zero-temperature transitions in a qualitatively correct way, even if frustration is present and other methods such as quantum Monte Carlo fail.Comment: 8 pages, 12 Postscipt figures; Accepted for publication in World Scientifi

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 figure

Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems

We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. We use the coupled cluster method (CCM) for high orders of approximation (up to LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to calculate ground-state properties. The role of quantum fluctuations is examined by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral transition within the same model. We find clear evidence that quantum fluctuations prefer collinear order and that they may favour a first order transition instead of a second order transition in case of no quantum fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.

Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities

In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed {\it et al.} [arXiv:1004.4323v1].Comment: 4 pages, 5 figure