142 research outputs found
A time-dependent variational principle for dissipative dynamics
We extend the time-dependent variational principle to the setting of
dissipative dynamics. This provides a locally optimal (in time) approximation
to the dynamics of any Lindblad equation within a given variational manifold of
mixed states. In contrast to the pure-state setting there is no canonical
information geometry for mixed states and this leads to a family of possible
trajectories --- one for each information metric. We focus on the case of the
operationally motivated family of monotone riemannian metrics and show further,
that in the particular case where the variational manifold is given by the set
of fermionic gaussian states all of these possible trajectories coincide. We
illustrate our results in the case of the Hubbard model subject to spin
decoherence.Comment: Published versio
Ground States of Fermionic lattice Hamiltonians with Permutation Symmetry
We study the ground states of lattice Hamiltonians that are invariant under
permutations, in the limit where the number of lattice sites, N -> \infty. For
spin systems, these are product states, a fact that follows directly from the
quantum de Finetti theorem. For fermionic systems, however, the problem is very
different, since mode operators acting on different sites do not commute, but
anti-commute. We construct a family of fermionic states, \cal{F}, from which
such ground states can be easily computed. They are characterized by few
parameters whose number only depends on M, the number of modes per lattice
site. We also give an explicit construction for M=1,2. In the first case,
\cal{F} is contained in the set of Gaussian states, whereas in the second it is
not. Inspired by that constructions, we build a set of fermionic variational
wave functions, and apply it to the Fermi-Hubbard model in two spatial
dimensions, obtaining results that go beyond the generalized Hartree-Fock
theory.Comment: 23 pages, published versio
Generalized Hartree Fock Theory for Dispersion Relations of Interacting Fermionic Lattice Systems
We study the variational solution of generic interacting fermionic lattice
systems using fermionic Gaussian states and show that the process of
"gaussification", leading to a nonlinear closed equation of motion for the
covariance matrix, is locally optimal in time by relating it to the
time-dependent variational principle. By linearising our nonlinear equation of
motion around the ground-state fixed point we describe a method to study
low-lying excited states leading to a variational method to determine the
dispersion relations of generic interacting fermionic lattice systems. This
procedure is applied to study the attractive and repulsive Hubbard model on a
two-dimensional lattice
Pairing in fermionic systems: A quantum information perspective
The notion of "paired" fermions is central to important condensed matter
phenomena such as superconductivity and superfluidity. While the concept is
widely used and its physical meaning is clear there exists no systematic and
mathematical theory of pairing which would allow to unambiguously characterize
and systematically detect paired states. We propose a definition of pairing and
develop methods for its detection and quantification applicable to current
experimental setups. Pairing is shown to be a quantum correlation different
from entanglement, giving further understanding in the structure of highly
correlated quantum systems. In addition, we will show the resource character of
paired states for precision metrology, proving that the BCS states allow phase
measurements at the Heisenberg limit.Comment: 23 pages, 4 figure
Generating topological order from a 2D cluster state using a duality mapping
In this paper we prove, extend and review possible mappings between the
two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and
Kitaev's toric code model. We introduce a two-dimensional duality
transformation to map the two-dimensional lattice cluster state into the
topologically-ordered Wen model. Then, we subsequently investigates how this
mapping could be achieved physically, which allows us to discuss the rate at
which a topologically ordered system can be achieved. Next, using a lattice
fermionization method, Wen's model is mapped into a series of one-dimensional
Ising interactions. Considering the boundary terms with this mapping then
reveals how the Ising chains interact with one another. The relationships
discussed in this paper allow us to consider these models from two different
perspectives: From the perspective of condensed matter physics these mappings
allow us to learn more about the relation between the ground state properties
of the four different models, such as their entanglement or topological
structure. On the other hand, we take the duality of these models as a starting
point to address questions related to the universality of their ground states
for quantum computation.Comment: 5 Figure
Quantum simulations under translational symmetry
We investigate the power of quantum systems for the simulation of Hamiltonian
time evolutions on a cubic lattice under the constraint of translational
invariance. Given a set of translationally invariant local Hamiltonians and
short range interactions we determine time evolutions which can and those that
can not be simulated. Whereas for general spin systems no finite universal set
of generating interactions is shown to exist, universality turns out to be
generic for quadratic bosonic and fermionic nearest-neighbor interactions when
supplemented by all translationally invariant on-site Hamiltonians.Comment: 9 pages, 2 figures, references added, minor change
Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods
We present numerical methods to solve the Generalized Hartree-Fock theory for
fermionic systems in lattices, both in thermal equilibrium and out of
equilibrium. Specifically, we show how to determine the covariance matrix
corresponding to the Fermionic Gaussian state that optimally approximates the
quantum state of the fermions. The methods apply to relatively large systems,
since their complexity only scales quadratically with the number of lattice
sites. Moreover, they are specially suited to describe inhomogenous systems, as
those typically found in recent experiments with atoms in optical lattices, at
least in the weak interaction regime. As a benchmark, we have applied them to
the two-dimensional Hubbard model on a 10x10 lattice with and without an
external confinement.Comment: 16 pages, 22 figure
The genomes of two key bumblebee species with primitive eusocial organization
Background: The shift from solitary to social behavior is one of the major evolutionary transitions. Primitively eusocial bumblebees are uniquely placed to illuminate the evolution of highly eusocial insect societies. Bumblebees are also invaluable natural and agricultural pollinators, and there is widespread concern over recent population declines in some species. High-quality genomic data will inform key aspects of bumblebee biology, including susceptibility to implicated population viability threats. Results: We report the high quality draft genome sequences of Bombus terrestris and Bombus impatiens, two ecologically dominant bumblebees and widely utilized study species. Comparing these new genomes to those of the highly eusocial honeybee Apis mellifera and other Hymenoptera, we identify deeply conserved similarities, as well as novelties key to the biology of these organisms. Some honeybee genome features thought to underpin advanced eusociality are also present in bumblebees, indicating an earlier evolution in the bee lineage. Xenobiotic detoxification and immune genes are similarly depauperate in bumblebees and honeybees, and multiple categories of genes linked to social organization, including development and behavior, show high conservation. Key differences identified include a bias in bumblebee chemoreception towards gustation from olfaction, and striking differences in microRNAs, potentially responsible for gene regulation underlying social and other traits. Conclusions: These two bumblebee genomes provide a foundation for post-genomic research on these key pollinators and insect societies. Overall, gene repertoires suggest that the route to advanced eusociality in bees was mediated by many small changes in many genes and processes, and not by notable expansion or depauperation
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