3,375 research outputs found
Variational-Correlations Approach to Quantum Many-body Problems
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed
Three dimensional resonating valence bond liquids and their excitations
We show that there are two types of RVB liquid phases present in
three-dimensional quantum dimer models, corresponding to the deconfining phases
of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite
cubic lattice and is the generalization of the critical point in the square
lattice quantum dimer model found originally by Rokhsar and Kivelson. The
latter exists on the non-bipartite face-centred cubic lattice and generalizes
the RVB phase found earlier by us on the triangular lattice. We discuss the
excitation spectrum and the nature of the ordering in both cases. Both phases
exhibit gapped spinons. In the U(1) case we find a collective, linearly
dispersing, transverse excitation, which is the photon of the low energy
Maxwell Lagrangian and we identify the ordering as quantum order in Wen's
sense. In the Z_2 case all collective excitations are gapped and, as in d=2,
the low energy description of this topologically ordered state is the purely
topological BF action. As a byproduct of this analysis, we unearth a further
gapless excitation, the pi0n, in the square lattice quantum dimer model at its
critical point.Comment: 9 pages, 2 figure
Fractionalized topological insulators from frustrated spin models in three dimensions
We present a theory of three dimensional fractionalized topological
insulators in the form of U(1) spin liquids with gapped fermionic spinons in
the bulk and topologically protected gapless spinon surface states. Starting
from a spin-1/2 model on a pyrochlore lattice, with frustrated
antiferromagnetic and ferromagnetic exchange interactions, we show that
decomposition of the latter interactions, within slave-fermion representation
of the spins, can naturally give rise to an emergent spin-orbit coupling for
the spinons. This stabilizes a fractionalized topological insulators which also
have bulk bond spin-nematic order. Finally, we describe the low energy
properties of these states.Comment: 10 page
Routing on the Visibility Graph
We consider the problem of routing on a network in the presence of line
segment constraints (i.e., obstacles that edges in our network are not allowed
to cross). Let be a set of points in the plane and let be a set of
non-crossing line segments whose endpoints are in . We present two
deterministic 1-local -memory routing algorithms that are guaranteed to
find a path of at most linear size between any pair of vertices of the
\emph{visibility graph} of with respect to a set of constraints (i.e.,
the algorithms never look beyond the direct neighbours of the current location
and store only a constant amount of additional information). Contrary to {\em
all} existing deterministic local routing algorithms, our routing algorithms do
not route on a plane subgraph of the visibility graph. Additionally, we provide
lower bounds on the routing ratio of any deterministic local routing algorithm
on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the
28th International Symposium on Algorithms and Computation (ISAAC 2017).
Final version appeared in the Journal of Computational Geometr
Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments
We develop a quantum field theoretical framework to analytically study the
three-body constrained Bose-Hubbard model beyond mean field and non-interacting
spin wave approximations. It is based on an exact mapping of the constrained
model to a theory with two coupled bosonic degrees of freedom with polynomial
interactions, which have a natural interpretation as single particles and
two-particle states. The procedure can be seen as a proper quantization of the
Gutzwiller mean field theory. The theory is conveniently evaluated in the
framework of the quantum effective action, for which the usual symmetry
principles are now supplemented with a ``constraint principle'' operative on
short distances. We test the theory via investigation of scattering properties
of few particles in the limit of vanishing density, and we address the
complementary problem in the limit of maximum filling, where the low lying
excitations are holes and di-holes on top of the constraint induced insulator.
This is the first of a sequence of two papers. The application of the formalism
to the many-body problem, which can be realized with atoms in optical lattices
with strong three-body loss, is performed in a related work [14].Comment: 21 pages, 5 figure
- …