474 research outputs found
From exotic phases to microscopic Hamiltonians
We report recent analytical progress in the quest for spin models realising
exotic phases. We focus on the question of `reverse-engineering' a local, SU(2)
invariant S=1/2 Hamiltonian to exhibit phases predicted on the basis of
effective models, such as large-N or quantum dimer models. This aim is to
provide a point-of-principle demonstration of the possibility of constructing
such microscopic lattice Hamiltonians, as well as to complement and guide
numerical (and experimental) approaches to the same question. In particular, we
demonstrate how to utilise peturbed Klein Hamiltonians to generate effective
quantum dimer models. These models use local multi-spin interactions and, to
obtain a controlled theory, a decoration procedure involving the insertion of
Majumdar-Ghosh chainlets on the bonds of the lattice. The phases we thus
realise include deconfined resonating valence bond liquids, a devil's staircase
of interleaved phases which exhibits Cantor deconfinement, as well as a
three-dimensional U(1) liquid phase exhibiting photonic excitations.Comment: Invited talk at Peyresq Workshop on "Effective models for
low-dimensional strongly correlated systems". Proceedings to be published by
AIP. v2: references adde
Quantum Hall Skyrmions with Higher Topological Charge
We have investigated quantum Hall skyrmions at filling factor \nu=1 carrying
more than one unit of topological, and hence electric, charge. Using a
combination of analytic and numerical methods we find the counterintuitive
result that when the Zeeman energy is tuned to values much smaller than the
interaction energy (g \mu_B B/(e^2/\epsilon\ell) < 9*10^{-5}),the creation
energy of a charge two skyrmion becomes less than twice the creation energy of
a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged
skyrmions are stable to further accretion of charge and exhibit a 10% larger
spin per unit charge than charge one skyrmions which would, in principle,
signal this pairing.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, Rapid Communication
Nature of the spin liquid state of the Hubbard model on honeycomb lattice
Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a
spin liquid phase (SL) that intervenes between the antiferromagnetic and
semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To
better understand the nature of this exotic phase, we study the quantum
spin model on the honeycomb lattice, which provides an effective
description of the Mott insulating region of the Hubbard model. Employing the
variational Monte Carlo approach, we analyze the phase diagram of the model,
finding a phase transition between antiferromagnet and an unusual SL
state at , which we identify as the SL phase of the
Hubbard model. At higher we find a transition to a
dimerized state with spontaneously broken rotational symmetry.Comment: 5 pages, 6 figure
Diagnosing Deconfinement and Topological Order
Topological or deconfined phases are characterized by emergent, weakly
fluctuating, gauge fields. In condensed matter settings they inevitably come
coupled to excitations that carry the corresponding gauge charges which
invalidate the standard diagnostic of deconfinement---the Wilson loop. Inspired
by a mapping between symmetric sponges and the deconfined phase of the
gauge theory, we construct a diagnostic for deconfinement that has the
interpretation of a line tension. One operator version of this diagnostic turns
out to be the Fredenhagen-Marcu order parameter known to lattice gauge
theorists and we show that a different version is best suited to condensed
matter systems. We discuss generalizations of the diagnostic, use it to
establish the existence of finite temperature topological phases in
dimensions and show that multiplets of the diagnostic are useful in settings
with multiple phases such as gauge theories with charge matter.
[Additionally we present an exact reduction of the partition function of the
toric code in general dimensions to a well studied problem.]Comment: 11 pages, several figure
Dipolar spin correlations in classical pyrochlore magnets
We study spin correlations for the highly frustrated classical pyrochlore
lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture
that a local constraint obeyed by the extensively degenerate ground states
dictates a dipolar form for the asymptotic spin correlations, at all N 2
for which the system is paramagnetic down to T=0. We verify this conjecture in
the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion
about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an
excellent fit, at all distances, to the correlators at N=3 and even at N=1.
Thus we obtain a simple analytical expression also for the correlations of the
equivalent models of spin ice and cubic water ice, I_h.Comment: 4 pages revtex
Skyrmions in Higher Landau Levels
We calculate the energies of quasiparticles with large numbers of reversed
spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than
or equals 1. We find, in contrast with the known result for filling factor
equals 1 (k = 0), that these quasiparticles always have higher energy than the
fully polarized ones and hence are not the low energy charged excitations, even
at small Zeeman energies. It follows that skyrmions are the relevant
quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe
Biot-Savart correlations in layered superconductors
We discuss the superconductor to normal phase transition in an
infinite-layered type-II superconductor in the limit where the Josephson
coupling between layers is negligible. We model each layer as a neutral gas of
thermally excited pancake vortices. We assume the dominant interaction between
vortices in the same and in different layers is the electromagnetic interaction
between the screening currents induced by these vortices. Our main result,
obtained by exactly solving the leading order renormalization group flow, is
that the phase transition in this model is a Kosterlitz--Thouless transition
despite being a three--dimensional system. While the transition itself is
driven by the unbinding of two-dimensional pancake vortices, an RG analysis of
the low temperature phase and a mean-field theory of the high temperature phase
reveal that both phases possess three-dimensional correlations. An experimental
consequence of this is that the jump in the measured in-plane superfluid
stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will
receive a small non--universal correction (of order 1% in
BiSrCaCuO). This overall picture places some claims
expressed in the literature on a more secure analytical footing and also
resolves some conflicting views.Comment: 16 pages, 2 figures; minor typos corrected, references adde
Supersymmetric Model of Spin-1/2 Fermions on a Chain
In recent work, N=2 supersymmetry has been proposed as a tool for the
analysis of itinerant, correlated fermions on a lattice. In this paper we
extend these considerations to the case of lattice fermions with spin 1/2 . We
introduce a model for correlated spin-1/2 fermions with a manifest N=4
supersymmetry, and analyze its properties. The supersymmetric ground states
that we find represent holes in an anti-ferromagnetic background.Comment: 15 pages, 10 eps figure
SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
We construct a family of rotationally invariant, local, S=1/2 Klein
Hamiltonians on various lattices that exhibit ground state manifolds spanned by
nearest-neighbor valence bond states. We show that with selected perturbations
such models can be driven into phases modeled by well understood quantum dimer
models on the corresponding lattices. Specifically, we show that the
perturbation procedure is arbitrarily well controlled by a new parameter which
is the extent of decoration of the reference lattice. This strategy leads to
Hamiltonians that exhibit i) RVB phases in two dimensions, ii) U(1) RVB
phases with a gapless ``photon'' in three dimensions, and iii) a Cantor
deconfined region in two dimensions. We also construct two models on the
pyrochlore lattice, one model exhibiting a RVB phase and the other a U(1)
RVB phase.Comment: 16 pages, 15 figures; 1 figure and some references added; some minor
typos fixe
Many skyrmion wave functions and skyrmion statistics in quantum Hall ferromagnets
We determine the charge and statistical angle of skyrmions in quantum Hall
ferromagnets by performing Berry phase calculations based on the microscopic
variational wave functions for many-skyrmion states. We find, in contradiction
to a recent claim by Dziarmaga, that both the charge and the statistical angle
of a skyrmion are independent of its spin (size), and are identical to those of
Laughlin quasiparticles at the same filling factor. We discuss some subtleties
in the use of these variational wave functions.Comment: 11 pages, RevTex, no figure. Accepted in Phys. Rev. B, Rapid
Communication
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