413 research outputs found
Non-rigid hole band in the extended t-J model
The dispersion of one hole in an extended - model with additional
hopping terms to second and third nearest neighbours and a frustration term in
the exchange part has been investigated. Two methods, a Green's function
projection technique describing a magnetic polaron of minimal size and the
exact diagonalization of a lattice, have been applied, showing reasonable
agreement among each other. Using additional hopping integrals which are
characteristic for the CuO plane in cuprates we find in the nonfrustrated
case an isotropic minimum of the dispersion at the point in
-space in good coincidence with recent angle-resolved photoemission results
for the insulating compound SrCuOCl. Including frustration or
finite temperature which shall simulate the effect of doping, the dispersion is
drastically changed such that a flat region and an extended saddle point may be
observed between and in agreement with experimental
results for the optimally doped cuprates.Comment: 14 pages, LaTeX, 6 figures on request, submitted to Zeitschrift fuer
Physi
The DSUB Approximation Scheme for the Coupled Cluster Method and Applications to Quantum Magnets
A new approximate scheme, DSUB, is described for the coupled cluster
method. We then apply it to two well-studied (spin-1/2 Heisenberg
antiferromagnet) spin-lattice models, namely: the and the models on
the square lattice in two dimensions. Results are obtained in each case for the
ground-state energy, the sublattice magnetization and the quantum critical
point. They are in good agreement with those from such alternative methods as
spin-wave theory, series expansions, quantum Monte Carlo methods and those from
the CCM using the LSUB scheme.Comment: 18 pages, 10 figure
Modeling host-associating microbes under selection
The concept of fitness is often reduced to a single component, such as the replication rate in a given habitat. For species with multi-step life cycles, this can be an unjustified oversimplification, as every step of the life cycle can contribute to the overall reproductive success in a specific way. In particular, this applies to microbes that spend part of their life cycles associated to a host. In this case, there is a selection pressure not only on the replication rates, but also on the phenotypic traits associated to migrating from the external environment to the host and vice-versa (i.e., the migration rates). Here, we investigate a simple model of a microbial lineage living, replicating, migrating and competing in and between two compartments: a host and an environment. We perform a sensitivity analysis on the overall growth rate to determine the selection gradient experienced by the microbial lineage. We focus on the direction of selection at each point of the phenotypic space, defining an optimal way for the microbial lineage to increase its fitness. We show that microbes can adapt to the two-compartment life cycle through either changes in replication or migration rates, depending on the initial values of the traits, the initial distribution across the two compartments, the intensity of competition, and the time scales involved in the life cycle versus the time scale of adaptation (which determines the adequate probing time to measure fitness). Overall, our model provides a conceptual framework to study the selection on microbes experiencing a host-associated life cycle
Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
We study the ground-state properties of the spin-half Heisenberg
antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact
diagonalization and a variational mean-field approach. We find evidence that
the star lattice is (besides the \kagome lattice) a second candidate among the
11 uniform Archimedean lattices where quantum fluctuations in combination with
frustration lead to a quantum paramagnetic ground state. Although the classical
ground state of the Heisenberg antiferromagnet on the star exhibits a huge
non-trivial degeneracy like on the \kagome lattice, its quantum ground state is
most likely dimerized with a gap to all excitations. Finally, we find several
candidates for plateaux in the magnetization curve as well as a macroscopic
magnetization jump to saturation due to independent localized magnon states.Comment: new extended version (6 pages, 6 figures) as published in Physical
Review
Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
Using the coupled cluster method for high orders of approximation and Lanczos
exact diagonalization we study the ground-state phase diagram of a quantum
spin-1/2 J1-J2 model on the square lattice with plaquette structure. We
consider antiferromagnetic (J1>0) as well as ferromagnetic (J1<0)
nearest-neighbor interactions together with frustrating antiferromagnetic
next-nearest-neighbor interaction J2>0. The strength of inter-plaquette
interaction lambda varies between lambda=1 (that corresponds to the uniform
J1-J2 model) and lambda=0 (that corresponds to isolated frustrated 4-spin
plaquettes). While on the classical level (s \to \infty) both versions of
models (i.e., with ferro- and antiferromagnetic J1) exhibit the same
ground-state behavior, the ground-state phase diagram differs basically for the
quantum case s=1/2. For the antiferromagnetic case (J1 > 0) Neel
antiferromagnetic long-range order at small J2/J1 and lambda \gtrsim 0.47 as
well as collinear striped antiferromagnetic long-range order at large J2/J1 and
lambda \gtrsim 0.30 appear which correspond to their classical counterparts.
Both semi-classical magnetic phases are separated by a nonmagnetic quantum
paramagnetic phase. The parameter region, where this nonmagnetic phase exists,
increases with decreasing of lambda. For the ferromagnetic case (J1 < 0) we
have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of
J2 this classical phase gives way for a semi-classical plaquette phase, where
the plaquette block spins of length s=2 are antiferromagnetically long-range
ordered. Further increasing of J2 then yields collinear striped
antiferromagnetic long-range order for lambda \gtrsim 0.38, but a nonmagnetic
quantum paramagnetic phase lambda \lesssim 0.38.Comment: 10 pages, 15 figure
High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaVO
The coupled cluster method (CCM) is a method of quantum many-body theory that
may provide accurate results for the ground-state properties of lattice quantum
spin systems even in the presence of strong frustration and for lattices of
arbitrary spatial dimensionality. Here we present a significant extension of
the method by introducing a new approach that allows an efficient
parallelization of computer codes that carry out ``high-order'' CCM
calculations. We find that we are able to extend such CCM calculations by an
order of magnitude higher than ever before utilized in a high-order CCM
calculation for an antiferromagnet. Furthermore, we use only a relatively
modest number of processors, namely, eight. Such very high-order CCM
calculations are possible {\it only} by using such a parallelized approach. An
illustration of the new approach is presented for the ground-state properties
of a highly frustrated two-dimensional magnetic material, CaVO. Our
best results for the ground-state energy and sublattice magnetization for the
pure nearest-neighbor model are given by and ,
respectively, and we predict that there is no N\'eel ordering in the region
. These results are shown to be in excellent agreement
with the best results of other approximate methods.Comment: 4 page
Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum -- model on the square lattice
We study the zero-temperature phase diagram of the
-- Heisenberg model for spin-1 particles on an
infinite square lattice interacting via nearest-neighbour () and
next-nearest-neighbour () bonds. Both bonds have the same -type
anisotropy in spin space. The effects on the quasiclassical N\'{e}el-ordered
and collinear stripe-ordered states of varying the anisotropy parameter
is investigated using the coupled cluster method carried out to high
orders. By contrast with the spin-1/2 case studied previously, we predict no
intermediate disordered phase between the N\'{e}el and collinear stripe phases,
for any value of the frustration , for either the -aligned () or -planar-aligned () states. The quantum phase
transition is determined to be first-order for all values of and
. The position of the phase boundary is determined
accurately. It is observed to deviate most from its classical position (for all values of ) at the Heisenberg isotropic point
(), where . By contrast, at the XY
isotropic point (), we find . In the
Ising limit () as expected.Comment: 20 pages, 5 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
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