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

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart

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