8 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
Extended Quantum Dimer Model and novel valence-bond phases
We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so
as to construct a concrete example of the model which exhibits the first-order
phase transition between different valence-bond solids suggested recently by
Batista and Trugman and look for the possibility of other exotic dimer states.
We show that our model contains three exotic valence-bond phases (herringbone,
checkerboard and dimer smectic) in the ground-state phase diagram and that it
realizes the phase transition from the staggered valence-bond solid to the
herringbone one. The checkerboard phase has four-fold rotational symmetry,
while the dimer smectic, in the absence of quantum fluctuations, has massive
degeneracy originating from partial ordering only in one of the two spatial
directions. A resonance process involving three dimers resolves this massive
degeneracy and dimer smectic gets ordered (order from disorder).Comment: 20 pages, 13 figures, accepted for publication in J. Stat. Mec
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
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
Loop condensation in the triangular lattice quantum dimer model
We study the mechanism of loop condensation in the quantum dimer model on the
triangular lattice. The triangular lattice quantum dimer model displays a
topologically ordered quantum liquid phase in addition to conventionally
ordered phases with broken symmetry. In the context of systems with extended
loop-like degrees of freedom, the formation of such topological order can be
described in terms of loop condensation. Using Monte Carlo calculations with
local and directed-loop updates, we compute geometric properties of the
transition graph loop distributions of several triangular lattice quantum dimer
wavefunctions that display dimer-liquid to dimer-crystal transitions and
characterize these in terms of loop condensation.Comment: 22 pages, 12 figures, fixed references and minor typo
SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
16 pages, 15 figures; 1 figure and some references added; some minor typos fixedWe 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
Magnetization process of spin ice in a [111] magnetic field
13 pages, 13 figuresSpin ice in a magnetic field in the [111] direction displays two magnetization plateaux, one at saturation and an intermediate one with finite entropy. We study the crossovers between the different regimes from a point of view of (entropically) interacting defects. We develop an analytical theory for the nearest-neighbor spin ice model, which covers most of the magnetization curve. We find that the entropy is non-monotonic, exhibiting a giant spike between the two plateaux. This regime is described by a monomer-dimer model with tunable fugacities. At low fields, we develop an RG treatment for the extended string defects, and we compare our results to extensive Monte Carlo simulations. We address the implications of our results for cooling by adiabatic (de)magnetization