32 research outputs found
Universality and tails of long range interactions in one dimension
Long-range interactions and, in particular, two-body potentials with
power-law long-distance tails are ubiquitous in nature. For two bosons or
fermions in one spatial dimension, the latter case being formally equivalent to
three-dimensional -wave scattering, we show how generic asymptotic
interaction tails can be accounted for in the long-distance limit of scattering
wave functions. This is made possible by introducing a generalisation of the
collisional phase shifts to include space dependence. We show that this
distance dependence is universal, in that it does not depend on short-distance
details of the interaction. The energy dependence is also universal, and is
fully determined by the asymptotic tails of the two-body potential. As an
important application of our findings, we describe how to eliminate finite-size
effects with long-range potentials in the calculation of scattering phase
shifts from exact diagonalisation. We show that even with moderately small
system sizes it is possible to accurately extract phase shifts that would
otherwise be plagued with finite-size errors. We also consider multi-channel
scattering, focusing on the estimation of open channel asymptotic interaction
strengths via finite-size analysis.Comment: 7 pages, 3 figure
Few-Body Route to One-Dimensional Quantum Liquids
Gapless many-body quantum systems in one spatial dimension are universally
described by the Luttinger liquid effective theory at low energies.
Essentially, only two parameters enter the effective low-energy description,
namely the speed of sound and the Luttinger parameter. These are highly system
dependent and their calculation requires accurate non-perturbative solutions of
the many-body problem. Here, we present a simple method that only uses
collisional information to extract the low-energy properties of these systems.
Our results are in remarkable agreement with available results for integrable
models and from large scale Monte Carlo simulations of one-dimensional helium
and hydrogen isotopes. Moreover, we estimate theoretically the critical point
for spinodal decomposition in one-dimensional helium-4, and show that the
exponent governing the divergence of the Luttinger parameter near the critical
point is exactly 1/2, in excellent agreement with Monte Carlo simulations.Comment: 8 pages, 6 figures, including supplementary materia
Constructive role of dissipation for driven coupled bosonic modes
We theoretically investigate a system of two coupled bosonic modes subject to
both dissipation and external driving. We show that in the steady state the
degree of entanglement between the coupled bosonic modes can be enhanced by
dissipation. The non-monotonic dependence of entanglement on the decay rates is
observed when the bosonic modes are asymmetrically coupled to their local
baths. This counterintuitive result opens a new way to better understand the
interplay between noise and coherence in continuous variable systems driven
away from equilibrium.Comment: 4.5 pages. Published version (with minor modifications
Markovian evolution of strongly coupled harmonic oscillators
We investigate how to model Markovian evolution of coupled harmonic
oscillators, each of them interacting with a local environment. When the
coupling between the oscillators is weak, dissipation may be modeled using
local Lindblad terms for each of the oscillators in the master equation, as is
commonly done. When the coupling between oscillators is strong, this model may
become invalid. We derive a master equation for two coupled harmonic
oscillators which are subject to individual heat baths modeled by a collection
of harmonic oscillators, and show that this master equation in general contains
non-local Lindblad terms. We compare the resulting time evolution with that
obtained for dissipation through local Lindblad terms for each individual
oscillator, and show that the evolution is different in the two cases. In
particular, the two descriptions give different predictions for the steady
state and for the entanglement between strongly coupled oscillators. This shows
that when describing strongly coupled harmonic oscillators, one must take great
care in how dissipation is modeled, and that a description using local Lindblad
terms may fail. This may be particularly relevant when attempting to generate
entangled states of strongly coupled quantum systems.Comment: 11 pages, 4 figures, significantly revised and close to the published
versio
Investigating the generality of time-local master equations
Time-local master equations are more generally applicable than is often
recognised, but at first sight it would seem that they can only safely be used
in time intervals where the time evolution is invertible. Using the
Jaynes-Cummings model, we here construct an explicit example where two
different Hamiltonians, corresponding to two different non-invertible and
non-Markovian time evolutions, will lead to arbitrarily similar time-local
master equations. This illustrates how the time-local master equation on its
own in this case does not uniquely determine the time evolution. The example is
nevertheless artificial in the sense that a rapid change in (at least) one of
the Hamiltonians is needed. The change must also occur at a very specific
instance in time. If a Hamiltonian is known not to have such very specific
behaviour, but is "physically well-behaved", then one may conjecture that a
time-local master equation also determines the time evolution when it is not
invertible.Comment: 7 pages, 6 figure
Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice
We investigate the properties of an edge-centered honeycomb lattice, and show
that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at
different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1).
This five-band system is the simplest lattice that can support simultaneously
the two different paradigmatic Dirac-Weyl fermions with half-integer spin and
integer spin. We demonstrate that these pseudo-relativistic structures,
including a flat band at half-filling, can be deduced from the underlying
Kagome sublattice. We further show that the signatures of the two kinds of
relativistic fermions can be clearly revealed by several perturbations, such as
a uniform magnetic field, a Haldane-type spin-orbit term, and charge density
waves. We comment on the possibility to probe the similarities and differences
between the two kinds of relativistic fermions, or even to isolate them
individually. We present a realistic scheme to realize such a system using cold
atoms.Comment: published versio
Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor
Mobile spin impurity in an optical lattice
We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an
optical lattice for the limit of both strong repulsive contact interactions and
one dimension. In this limit, a polaronic-like behaviour is not expected, and
the physics is that of a magnon or impurity. While the charge degrees of
freedom of the system are frozen, the resulting tight-binding Hamiltonian for
the impurity's spin exhibits an intriguing structure that strongly depends on
the filling factor of the lattice potential. This filling dependency also
transfers to the nature of the interactions for the case of two magnons and the
important spin balanced case. At low filling, and up until near unit filling,
the single impurity Hamiltonian faithfully reproduces a single-band,
quasi-homogeneous tight-binding problem. As the filling is increased and the
second band of the single particle spectrum of the periodic potential is
progressively filled, the impurity Hamiltonian, at low energies, describes a
single particle trapped in a multi-well potential. Interestingly, once the
first two bands are fully filled, the impurity Hamiltonian is a near-perfect
realisation of the Su-Schrieffer-Heeger model. Our studies, which go well
beyond the single-band approximation, that is, the Hubbard model, pave the way
for the realisation of interacting one-dimensional models of condensed matter
physics.Comment: 13 pages, 12 figures, accepted in New Journal of Physic