24 research outputs found
Hierarchical Mean-Field Theories in Quantum Statistical Mechanics
We present a theoretical framework and a calculational scheme to study the
coexistence and competition of thermodynamic phases in quantum statistical
mechanics. The crux of the method is the realization that the microscopic
Hamiltonian, modeling the system, can always be written in a hierarchical
operator language that unveils all symmetry generators of the problem and,
thus, possible thermodynamic phases. In general one cannot compute the
thermodynamic or zero-temperature properties exactly and an approximate scheme
named ``hierarchical mean-field approach'' is introduced. This approach treats
all possible competing orders on an equal footing. We illustrate the
methodology by determining the phase diagram and quantum critical point of a
bosonic lattice model which displays coexistence and competition between
antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.
Coupled Heisenberg antiferromagnetic chains in an effective staggered field
We present a systematic study of coupled Heisenberg antiferromagnetic
chains in an effective staggered field. We investigate several effects of the
staggered field in the {\em higher} ({\em two or three}) {\em dimensional} spin
system analytically. In particular, in the case where the staggered field and
the inter-chain interaction compete with each other, we predict, using
mean-field theory, a characteristic phase transition. The spin-wave theory
predicts that the behavior of the gaps induced by the staggered field is
different between the competitive case and the non-competitive case. When the
inter-chain interactions are sufficiently weak, we can improve the mean-field
phase diagram by using chain mean-field theory and the analytical results of
field theories. The ordered phase region predicted by the chain mean-field
theory is substantially smaller than that by the mean-field theory.Comment: 13pages, 12figures, to be published in PR
Antiferromagnetically coupled alternating spin chains
The effect of antiferromagnetic interchain coupling in alternating spin
(1,1/2) chains is studied by mean of a spin wave theory and density matrix
renormalization group (DMRG). In particular, two limiting cases are
investigated, the two-leg ladder and its two dimensional (2D) generalization.
Results of the ground state properties like energy, spin gap, magnetizations,
and correlation functions are reported for the whole range of the interchain
coupling . For the 2D case the spin wave results predict a smooth
dimensional crossover from 1D to 2D keeping the ground state always ordered.
For the ladder system, the DMRG results show that any drives the
system to a gapped ground state. Furthermore the behaviour of the correlation
functions closely resemble the uniform spin-1/2 ladder. For lower
than 0.3, however, the gap behaves quadratically as . Finally, it is argued that the behaviour of the spin gap for an
arbitrary number of mixed coupled spin chains is analogous to that of the
uniform spin-1/2 chains.Comment: 5 pages, 7 ps-figure