54 research outputs found
Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points
We determine the dynamical dimer correlation functions of quantum dimer
models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices
and the non-bipartite triangular lattice. Based on an algorithmic idea by
Henley, we simulate a stochastic process of classical dimer configurations in
continuous time and perform a stochastic analytical continuation to obtain the
dynamical correlations in momentum space and the frequency domain. This
approach allows us to observe directly the dispersion relations and the
evolution of the spectral intensity within the Brillouin zone beyond the
single-mode approximation. On the square lattice, we confirm analytical
predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0)
and further reveal the existence of shadow bands close to the wavevector (0,0).
On the cubic lattice the spectrum is also gapless but here only a single soft
mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The
soft mode has a quadratic dispersion at very long wavelength, but crosses over
to a linear behavior very rapidly. We believe this to be the remnant of the
linearly dispersing "photon" of the Coulomb phase. Finally the triangular
lattice is in a fully gapped liquid phase where the bottom of the dimer
spectrum exhibits a rich structure. At the M point the gap is minimal and the
spectral response is dominated by a sharp quasiparticle peak. On the other
hand, at the X point the spectral function is much broader. We sketch a
possible explanation based on the crossing of the coherent dimer excitations
into the two-vison continuum.Comment: 16 pages, 7 figures, published versio
Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
We study the antiferromagnetic spin-1/2 Heisenberg model on the highly
frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a
series expansion method. We propose a valence bond crystal with a 72 site unit
cell as a ground state that supports many, very low lying, singlet excitations.
Low energy spinons and triplons are confined to emergent lower-dimensional
motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite
temperature signatures, including an Ising transition, in the magnetic specific
heat due to a multistep breaking of discrete symmetries.Comment: 4 pages, 3 figure
Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
We show that the spin liquid phase of the half-filled Hubbard model on the
triangular lattice can be described by a pure spin model. This is based on a
high-order strong coupling expansion (up to order 12) using perturbative
continuous unitary transformations. The resulting spin model is consistent with
a transition from three-sublattice long-range magnetic order to an insulating
spin liquid phase, and with a jump of the double occupancy at the transition.
Exact diagonalizations of both models show that the effective spin model is
quantitatively accurate well into the spin liquid phase, and a comparison with
the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon
Fermi surface.Comment: 4 pages, 4 figures, published versions with additional dat
Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
After reviewing the concept of vison excitations in Z_2 dimer liquids, we
study the liquid-crystal transition of the Quantum Dimer Model on the
triangular lattice by means of a semiclassical spin-wave approximation to the
dispersion of visons in the context of a "soft-dimer" version of the model.
This approach captures some important qualitative features of the transition:
continuous nature of the transition, linear dispersion at the critical point,
and \sqrt{12}x\sqrt{12} symmetry-breaking pattern. In a second part, we present
a variational calculation of the vison dispersion relation at the RK point
which reproduces the qualitative shape of the dispersion relation and the order
of magnitude of the gap. This approach provides a simple but reliable
approximation of the vison wave functions at the RK point.Comment: 12 pages, 10 figures. v2: minor changes, to appear in Phys. Rev.
Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2
Motivated by the recent discovery of the spin tube
[(CuCltachH)Cl]Cl, we investigate the properties of a frustrated
three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings.
We pay special attention to the evolution of the properties from weak to strong
inter-ring coupling and show on the basis of extensive density matrix
renormalization group and exact diagonalization calculations that the system
undergoes a first-order phase transition between a dimerized gapped phase at
weak coupling that can be described by the usual spin-chirality model and a
gapless critical phase at strong coupling that can be described by an effective
spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in
the gapped phase and slightly beyond. The implications for
[(CuCltachH)Cl]Cl are discussed, with the conclusion that this
system behaves essentially as a spin-3/2 chain.Comment: 8 pages, 9 figures, revised versio
Doped two-leg ladder with ring exchange
The effect of a ring exchange on doped two-leg ladders is investigated
combining exact diagonalization (ED) and density matrix renormalization group
(DMRG) computations. We focus on the nature and weights of the low energy
magnetic excitations and on superconducting pairing. The stability with respect
to this cyclic term of a remarkable resonant mode originating from a hole
pair-magnon bound state is examined. We also find that, near the zero-doping
critical point separating rung-singlet and dimerized phases, doping reopens a
spin gap.Comment: 5 pages, 7 figures, to appear in PR
Approximate eigenvalue determination of geometrically frustrated magnetic molecules
Geometrically frustrated magnetic molecules have attracted a lot of interest
in the field of molecular magnetism as well as frustrated Heisenberg
antiferromagnets. In this article we demonstrate how an approximate
diagonalization scheme can be used in order to obtain thermodynamic and
spectroscopic information about frustrated magnetic molecules. To this end we
theoretically investigate an antiferromagnetically coupled spin system with
cuboctahedral structure modeled by an isotropic Heisenberg Hamiltonian.Comment: 12 pages, 13 figures, submitted for a special issue of Condensed
Matter Physics (CMP
Approximating random quantum optimization problems
We report a cluster of results regarding the difficulty of finding
approximate ground states to typical instances of the quantum satisfiability
problem -QSAT on large random graphs. As an approximation strategy, we
optimize the solution space over `classical' product states, which in turn
introduces a novel autonomous classical optimization problem, PSAT, over a
space of continuous degrees of freedom rather than discrete bits. Our central
results are: (i) The derivation of a set of bounds and approximations in
various limits of the problem, several of which we believe may be amenable to a
rigorous treatment. (ii) A demonstration that an approximation based on a
greedy algorithm borrowed from the study of frustrated magnetism performs well
over a wide range in parameter space, and its performance reflects structure of
the solution space of random -QSAT. Simulated annealing exhibits
metastability in similar `hard' regions of parameter space. (iii) A
generalization of belief propagation algorithms introduced for classical
problems to the case of continuous spins. This yields both approximate
solutions, as well as insights into the free energy `landscape' of the
approximation problem, including a so-called dynamical transition near the
satisfiability threshold. Taken together, these results allow us to elucidate
the phase diagram of random -QSAT in a two-dimensional
energy-density--clause-density space.Comment: 14 pages, 9 figure
Coexistence of pairing gaps in three-component Fermi gases
We study a three-component superfluid Fermi gas in a spherically symmetric
harmonic trap using the Bogoliubov-deGennes method. We predict a coexistence
phase in which two pairing field order parameters are simultaneously nonzero,
in stark contrast to studies performed for trapped gases using local density
approximation. We also discuss the role of atom number conservation in the
context of a homogeneous system.Comment: Text revised, added two figures and three reference
- …