31 research outputs found
New quantum phase transitions in the two-dimensional J1-J2 model
We analyze the phase diagram of the frustrated Heisenberg antiferromagnet,
the J1-J2 model, in two dimensions. Two quantum phase transitions in the model
are already known: the second order transition from the Neel state to the spin
liquid state at (J_2/J_1)_{c2}=0.38, and the first order transition from the
spin liquid state to the collinear state at (J_2/J_1)_{c4}=0.60. We have found
evidence for two new second order phase transitions: the transition from the
spin columnar dimerized state to the state with plaquette type modulation at
(J_2/J_1)_{c3}=0.50(2), and the transition from the simple Neel state to the
Neel state with spin columnar dimerization at (J_2/J_1)_{c1}=0.34(4). We also
present an independent calculation of (J_2/J_1)_{c2}=0.38 using a new approach.Comment: 3 pages, 5 figures; added referenc
Suppression of Dimer Correlations in the Two-Dimensional - Heisenberg Model: an Exact Diagonalization Study
We present an exact diagonalization study of the ground state of the
spin-half model. Dimer correlation functions and the susceptibility
associated to the breaking of the translational invariance are calculated for
the and the clusters. These results -- especially when
compared to the one dimensional case, where the occurrence of a dimerized phase
for large enough frustration is well established -- suggest either a
homogeneous spin liquid or, possibly, a dimerized state with a rather small
order parameter
Phase Diagram of the Spin-Orbital model on the Square Lattice
We study the phase diagram of the spin-orbital model in both the weak and
strong limits of the quartic spin-orbital exchange interaction. This allows us
to study quantum phase transitions in the model and to approach from both sides
the most interesting intermediate-coupling regime and in particular the
SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al
[Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of
the system is a plaquette spin-orbital liquid. We argue that the state is more
complex. There is plaquette order, but it is anisotropic: bonds in one
direction are stronger than those in the perpendicular direction. This order is
somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg
spin model.Comment: 8 pages, 4 Postscript figure
Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet
We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.Comment: 7 pages, 11 figures, RevTeX minor changes made, Figure 6 correcte
Reduced density matrices and entanglement entropy in free lattice models
We review the properties of reduced density matrices for free fermionic or
bosonic many-particle systems in their ground state. Their basic feature is
that they have a thermal form and thus lead to a quasi-thermodynamic problem
with a certain free-particle Hamiltonian. We discuss the derivation of this
result, the character of the Hamiltonian and its eigenstates, the
single-particle spectra and the full spectra, the resulting entanglement and in
particular the entanglement entropy. This is done for various one- and
two-dimensional situations, including also the evolution after global or local
quenches.Comment: 33 pages, 18 figures, minor changes, references added. Review article
for the special issue "Entanglement entropy in extended systems" in J. Phys.
Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions
The ground states and excitations of two-dimensional insulating and doped
Mott insulators are described by a bond operator formalism. While the method
represents the degrees of freedom of an arbitrary antiferromagnet exactly, it
is especially suited to systems in which there is a natural pairing of sites
into bonds, as in states with spontaneous or explicit spin-Peierls order (or
bond-centered charge order). In the undoped insulator, as discussed previously,
we obtain both paramagnetic and magnetically-ordered states. We describe the
evolution of superconducting order in the ground state with increasing
doping--at low doping, the superconductivity is weak, can co-exist with
magnetic order, and there are no gapless spin 1/2 fermionic excitations; at
high doping, the magnetic order is absent and we obtain a BCS d-wave
superconductor with gapless spin 1/2, nodal fermions. We present the critical
theory describing the onset of these nodal fermionic excitations. We discuss
the evolution of the spin spectrum, and obtain regimes where a spin 1 exciton
contributes a sharp resonance in the dynamic spin susceptiblity. We also
discuss the experimental consequences of low-energy, dynamically fluctuating,
spin-Peierls order in an isotropic CuO_2 plane--we compute consequences for the
damping and dispersion of an optical phonon involving primarily the O ions, and
compare the results with recent neutron scattering measurements of phonon
spectra.Comment: 16 pages + 14 pages of appendices, 18 figures; (v3) expanded
discussion of theory and experimental implications; (v4) Removed some
introductory review discussion and moved it to cond-mat/010823
Quantum phases and phase transitions of Mott insulators
This article contains a theoretical overview of the physical properties of
antiferromagnetic Mott insulators in spatial dimensions greater than one. Many
such materials have been experimentally studied in the past decade and a half,
and we make contact with these studies. The simplest class of Mott insulators
have an even number of S=1/2 spins per unit cell, and these can be described
with quantitative accuracy by the bond operator method: we discuss their spin
gap and magnetically ordered states, and the transitions between them driven by
pressure or an applied magnetic field. The case of an odd number of S=1/2 spins
per unit cell is more subtle: here the spin gap state can spontaneously develop
bond order (so the ground state again has an even number of S=1/2 spins per
unit cell), and/or acquire topological order and fractionalized excitations. We
describe the conditions under which such spin gap states can form, and survey
recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase
transitions among these states and magnetically ordered states. We describe the
breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical
points, accompanied by the appearance of emergent gauge excitations.Comment: 51 pages, 13 figure
Low-energy fixed points of random Heisenberg models
The effect of quenched disorder on the low-energy and low-temperature
properties of various two- and three-dimensional Heisenberg models is studied
by a numerical strong disorder renormalization group method. For strong enough
disorder we have identified two relevant fixed points, in which the gap
exponent, omega, describing the low-energy tail of the gap distribution,
P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings
and the value of the spin. The dynamical behavior of non-frustrated random
antiferromagnetic models is controlled by a singlet-like fixed point, whereas
for frustrated models the fixed point corresponds to a large spin formation and
the gap exponent is given by omega ~ 0. Another type of universality classes is
observed at quantum critical points and in dimerized phases but no infinite
randomness behavior is found, in contrast to one-dimensional models.Comment: 11 pages RevTeX, eps-figs included, language revise