23 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
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
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
Some formal results for the valence bond basis
In a system with an even number of SU(2) spins, there is an overcomplete set
of states--consisting of all possible pairings of the spins into valence
bonds--that spans the S=0 Hilbert subspace. Operator expectation values in this
basis are related to the properties of the closed loops that are formed by the
overlap of valence bond states. We construct a generating function for spin
correlation functions of arbitrary order and show that all nonvanishing
contributions arise from configurations that are topologically irreducible. We
derive explicit formulas for the correlation functions at second, fourth, and
sixth order. We then extend the valence bond basis to include triplet bonds and
discuss how to compute properties that are related to operators acting outside
the singlet sector. These results are relevant to analytical calculations and
to numerical valence bond simulations using quantum Monte Carlo, variational
wavefunctions, or exact diagonalization.Comment: 22 pages, 14 figure
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