We study the T = 0 frustrated phase of the 1D quantum spin-1 2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.
In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a Néel model state with spins aligned in the z-direction, for both the ground-and excitedstate properties of the spin-half 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 XXZ model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUBm scheme in which we retain all k-body correlations defined on all possible locales of m adjacent lattice sites (k ≤ m).The "raw" CCM LSUBm 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 LSUBm results to the limit m → ∞ (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.
The coupled cluster method ͑CCM͒ is a well-known method of quantum many-body theory, and in this article we present an application of the CCM to the spin-half J 1 -J 2 quantum spin model with nearest-and next-nearest-neighbor interactions on the linear chain and the square lattice. We present results for ground-state expectation values of such quantities as the energy and the sublattice magnetization. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of J 2 /J 1 , of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (J 2 ϭ0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given by
The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are de6ned, which are specialized for the spin-lattice models. Good results are obtained for both groundstate and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.
With the increasing use of simulation for building design, test reference years (TRYs) are required for energy analyses and design summer years (DSYs) for assessing natural ventilation in the summer. Previously TRYs and DSYs only existed for three sites in the UK. Also the data was derived from weather data up to 1995. More sites were required and also updated data, as a number of warm years had occurred after 1995. The opportunity was also taken to improve the derivation of the TRY using just the Finkelstein-Schafer statistic and also to improve the algorithm for smoothing between months. New programs had to be written for filling missing values in the lower-quality raw data. This paper describes these programmes, the quality assurance procedures and analyses the years produced. A comparison is made between the 14 sites demonstrating the link between dry bulb temperature, solar radiation and latitude.
. Spin chains in a field: Crossover from quantum to classical behavior. Phys. Rev. B 32, 4703 (1985). It appears that calculations on significantly longer chains are required to observe with confidence the large-N asymptotic limiting behavior.
The icy satellites of the outer solar system are some of the most enigmatic and inspirational bodies in planetary science, in large part due to their astrobiological potential (Des Marais et al., 2008;Hendrix et al., 2019;B. E. Schmidt, 2020). Ongoing geological activity and geomorphological features indicative of persistent subsurface water reservoirs suggests that these ice-ocean worlds may house aqueous environments suitable for the formation and evolution of life (
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