The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation

The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the ground-state wave functions $|\Psi\rangle= e^S |\Phi\rangle$ which live in the "physical" Hilbert space ${\cal H}^{(P)}$ using an elementary ansatz for $|\Phi\rangle$ plus a formal expansion of $S$ in an operator basis of multi-configurational creation operators. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol $H$), which is self-adjoint in ${\cal H}^{(P)}$, to its effective lower-case isospectral avatar $\hat{h}=e^{-S} H e^S$, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian $\hat{h}$, which only appears manifestly non-Hermitian in its own ("friendly") Hilbert space ${\cal H}^{(F)}$. This goal is achieved via an ad hoc amendment of the inner product in ${\cal H}^{(F)}$, thereby yielding the third ("standard") Hilbert space ${\cal H}^{(S)}$. Due to the resulting exact unitary equivalence between the first and third spaces, ${\cal H}^{(P)}\sim {\cal H}^{(S)}$, the indistinguishability of predictions calculated in these alternative physical frameworks is guaranteed.Comment: 15 page

Phase Transitions in the Spin-Half J_1--J_2 Model

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. 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 = 0) 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 (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spin-half Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange bonds [J>0 (antiferromagnetic) and -∞<J'<∞] using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Ne´el model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Ne´el order to a finite-gap quantum disorderedphase for sufficiently large antiferromagnetic exchange constants J'>0. For frustrating ferromagnetic couplings J'<0 we find indications that quantum fluctuations favor a first-order phase transition from the Ne´el order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J'=0, which is equivalent to the honeycomb lattice, is treated more closely

Towards a coupled-cluster treatment of SU(N) lattice gauge field theory

A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU(N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Summer CO2 evasion from streams and rivers in the Kolyma River basin, north-east Siberia

Inland water systems are generally supersaturated in carbon dioxide (CO2) and are increasingly recognized as playing an important role in the global carbon cycle. The Arctic may be particularly important in this respect, given the abundance of inland waters and carbon contained in Arctic soils; however, a lack of trace gas measurements from small streams in the Arctic currently limits this understanding.We investigated the spatial variability of CO2 evasion during the summer low-flow period from streams and rivers in the northern portion of the Kolyma River basin in north-eastern Siberia. To this end, partial pressure of carbon dioxide (pCO2) and gas exchange velocities (k) were measured at a diverse set of streams and rivers to calculate CO2 evasion fluxes. We combined these CO2 evasion estimates with satellite remote sensing and geographic information system techniques to calculate total areal CO2 emissions. Our results show that small streams are substantial sources of atmospheric CO2 owing to high pCO2 and k, despite being a small portion of total inland water surface area. In contrast, large rivers were generally near equilibrium with atmospheric CO2. Extrapolating our findings across the Panteleikha-Ambolikha sub-watersheds demonstrated that small streams play a major role in CO2 evasion, accounting for 86% of the total summer CO2 emissions from inland waters within these two sub-watersheds. Further expansion of these regional CO2 emission estimates across time and space will be critical to accurately quantify and understand the role of Arctic streams and rivers in the global carbon budget