32 research outputs found
Spin-orbital quantum liquid on the honeycomb lattice
In addition to low-energy spin fluctuations, which distinguish them from band
insulators, Mott insulators often possess orbital degrees of freedom when
crystal-field levels are partially filled. While in most situations spins and
orbitals develop long-range order, the possibility for the ground state to be a
quantum liquid opens new perspectives. In this paper, we provide clear evidence
that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a
quantum spin-orbital liquid. The absence of any form of symmetry breaking -
lattice or SU(N) - is supported by a combination of semiclassical and numerical
approaches: flavor-wave theory, tensor network algorithm, and exact
diagonalizations. In addition, all properties revealed by these methods are
very accurately accounted for by a projected variational wave-function based on
the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that
state, correlations are algebraic because of the presence of a Dirac point at
the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the
honeycomb lattice is an algebraic quantum spin-orbital liquid. This model
provides a good starting point to understand the recently discovered
spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest
to choose optical lattices with honeycomb geometry in the search for quantum
liquids in ultra-cold four-color fermionic atoms.Comment: 10 pages, 7 figure
Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
We provide numerical evidence in favor of spontaneous chiral symmetry
breaking and the concomitant appearance of an Abelian chiral spin liquid for
three-component fermions on the triangular lattice described by an SU(3)
symmetric Hubbard model with hopping amplitude () and on-site
interaction . This chiral phase is stabilized in the Mott phase with one
particle per site in the presence of a uniform -flux per plaquette, and in
the Mott phase with two particles per site without any flux. Our approach
relies on effective spin models derived in the strong-coupling limit in powers
of for general SU and arbitrary uniform charge flux per plaquette,
which are subsequently studied using exact diagonalizations and variational
Monte Carlo simulations for , as well as exact diagonalizations of the
SU() Hubbard model on small clusters. Up to third order in , and for
the time-reversal symmetric cases (flux or ), the low-energy
description is given by the - model with Heisenberg coupling and real
ring exchange . The phase diagram in the full - parameter range
contains, apart from three already known, magnetically long-range ordered
phases, two previously unreported phases: i) a lattice nematic phase breaking
the lattice rotation symmetry and ii) a spontaneous time-reversal and parity
symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an
investigation that includes higher-order itinerancy effects supports the
presence of a phase transition inside the insulating region, occurring at
[] between the
three-sublattice magnetically ordered phase at small and this Abelian
chiral spin liquid.Comment: 21 pages, 23 figure
On the Critical Temperature of Non-Periodic Ising Models on Hexagonal Lattices
The critical temperature of layered Ising models on triangular and honeycomb
lattices are calculated in simple, explicit form for arbitrary distribution of
the couplings.Comment: to appear in Z. Phys. B., 8 pages plain TEX, 1 figure available upon
reques
Surface critical behavior of two-dimensional dilute Ising models
Ising models with nearest-neighbor ferromagnetic random couplings on a square
lattice with a (1,1) surface are studied, using Monte Carlo techniques and
star-tiangle transformation method. In particular, the critical exponent of the
surface magnetization is found to be close to that of the perfect model,
beta_s=1/2. The crossover from surface to bulk critical properties is
discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy
Percolation and Conduction in Restricted Geometries
The finite-size scaling behaviour for percolation and conduction is studied
in two-dimensional triangular-shaped random resistor networks at the
percolation threshold. The numerical simulations are performed using an
efficient star-triangle algorithm. The percolation exponents, linked to the
critical behaviour at corners, are in good agreement with the conformal
results. The conductivity exponent, t', is found to be independent of the shape
of the system. Its value is very close to recent estimates for the surface and
bulk conductivity exponents.Comment: 10 pages, 7 figures, TeX, IOP macros include
Numerical study of the critical behavior of the Ashkin-Teller model at a line defect
We consider the Ashkin-Teller model on the square lattice, which is
represented by two Ising models ( and ) having a four-spin
coupling of strength, , between them. We introduce an asymmetric
defect line in the system along which the couplings in the Ising model
are modified. In the Hamiltonian version of the model we study the scaling
behavior of the critical magnetization at the defect, both for and for
spins by density matrix renormalization. For we observe
identical scaling for and spins, whereas for one
model becomes locally ordered and the other locally disordered. This is
different of the critical behavior of the uncoupled model () and is
in contradiction with the results of recent field-theoretical calculations.Comment: 6 pages, 4 figure
Boundary critical behaviour of two-dimensional random Ising models
Using Monte Carlo techniques and a star-triangle transformation, Ising models
with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on
a square lattice with a (1,1) surface are studied near the phase transition.
Both surface and bulk critical properties are investigated. In particular, the
critical exponents of the surface magnetization, 'beta_1', of the correlation
length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are
analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.
Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study
singular quantities in the Griffiths phase of random quantum spin chains. For
the random transverse-field Ising spin chain we have extended Fisher's
analytical solution to the off-critical region and calculated the dynamical
exponent exactly. Concerning other random chains we argue by scaling
considerations that the RG method generally becomes asymptotically exact for
large times, both at the critical point and in the whole Griffiths phase. This
statement is checked via numerical calculations on the random Heisenberg and
quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include
Disorder Induced Phases in Higher Spin Antiferromagnetic Heisenberg Chains
Extensive DMRG calculations for spin S=1/2 and S=3/2 disordered
antiferromagnetic Heisenberg chains show a rather distinct behavior in the two
cases. While at sufficiently strong disorder both systems are in a random
singlet phase, we show that weak disorder is an irrelevant perturbation for the
S=3/2 chain, contrary to what expected from a naive application of the Harris
criterion. The observed irrelevance is attributed to the presence of a new
correlation length due to enhanced end-to-end correlations. This phenomenon is
expected to occur for all half-integer S > 1/2 chains. A possible phase diagram
of the chain for generic S is also discussed.Comment: 6 Pages and 6 figures. Final version as publishe
Surface critical behavior of random systems at the ordinary transition
We calculate the surface critical exponents of the ordinary transition
occuring in semi-infinite, quenched dilute Ising-like systems. This is done by
applying the field theoretic approach directly in d=3 dimensions up to the
two-loop approximation, as well as in dimensions. At
we extend, up to the next-to-leading order, the previous
first-order results of the expansion by Ohno and Okabe
[Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface
exponents are computed using Pade approximants extrapolating the perturbation
theory expansions. The obtained results indicate that the critical behavior of
semi-infinite systems with quenched bulk disorder is characterized by the new
set of surface critical exponents.Comment: 11 pages, 11 figure