3,957 research outputs found
Concurrence in collective models
We review the entanglement properties in collective models and their
relationship with quantum phase transitions. Focusing on the concurrence which
characterizes the two-spin entanglement, we show that for first-order
transition, this quantity is singular but continuous at the transition point,
contrary to the common belief. We also propose a conjecture for the concurrence
of arbitrary symmetric states which connects it with a recently proposed
criterion for bipartite entanglement.Comment: 8 pages, 2 figures, published versio
The Quantum Compass Model on the Square Lattice
Using exact diagonalizations, Green's function Monte Carlo simulations and
high-order perturbation theory, we study the low-energy properties of the
two-dimensional spin-1/2 compass model on the square lattice defined by the
Hamiltonian . When
, we show that, on clusters of dimension , the
low-energy spectrum consists of states which collapse onto each other
exponentially fast with , a conclusion that remains true arbitrarily close
to . At that point, we show that an even larger number of states
collapse exponentially fast with onto the ground state, and we present
numerical evidence that this number is precisely . We also extend
the symmetry analysis of the model to arbitrary spins and show that the
two-fold degeneracy of all eigenstates remains true for arbitrary half-integer
spins but does not apply to integer spins, in which cases eigenstates are
generically non degenerate, a result confirmed by exact diagonalizations in the
spin-1 case. Implications for Mott insulators and Josephson junction arrays are
briefly discussed.Comment: 8 pages, 8 figure
Finite-size scaling exponents and entanglement in the two-level BCS model
We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio
Direct observation of quantum phonon fluctuations in a one dimensional Bose gas
We report the first direct observation of collective quantum fluctuations in
a continuous field. Shot-to-shot atom number fluctuations in small sub-volumes
of a weakly interacting ultracold atomic 1D cloud are studied using \textit{in
situ} absorption imaging and statistical analysis of the density profiles. In
the cloud centers, well in the \textit{quantum quasicondensate} regime, the
ratio of chemical potential to thermal energy is , and,
owing to high resolution, up to 20% of the microscopically observed
fluctuations are quantum phonons. Within a non-local analysis at variable
observation length, we observe a clear deviation from a classical field
prediction, which reveals the emergence of dominant quantum fluctuations at
short length scales, as the thermodynamic limit breaks down.Comment: 4 pages, 3 figures (Supplementary material 3 pages, 3 figures
Simulation of large deviation functions using population dynamics
In these notes we present a pedagogical account of the population dynamics
methods recently introduced to simulate large deviation functions of dynamical
observables in and out of equilibrium. After a brief introduction on large
deviation functions and their simulations, we review the method of Giardin\`a
\emph{et al.} for discrete time processes and that of Lecomte \emph{et al.} for
the continuous time counterpart. Last we explain how these methods can be
modified to handle static observables and extract information about
intermediate times.Comment: Proceedings of the 10th Granada Seminar on Computational and
Statistical Physic
Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential
We consider a branching particle system where each particle moves as an
independent Brownian motion and breeds at a rate proportional to its distance
from the origin raised to the power , for . The asymptotic
behaviour of the right-most particle for this system is already known; in this
article we give large deviations probabilities for particles following
"difficult" paths, growth rates along "easy" paths, the total population growth
rate, and we derive the optimal paths which particles must follow to achieve
this growth rate.Comment: 56 pages, 1 figur
Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick
model by means of the Holstein-Primakoff representation of the spin operators
and the continuous unitary transformations method. This combination allows us
to compute analytically leading corrections to the ground state energy, the
gap, the magnetization, and the two-spin correlation functions. We also present
numerical calculations for large system size which confirm the validity of this
approach. Finally, we use these results to discuss the entanglement properties
of the ground state focusing on the (rescaled) concurrence that we compute in
the thermodynamical limit.Comment: 20 pages, 9 figures, published versio
Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
We establish a relation between several entanglement properties in the
Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins
embedded in a magnetic field. We provide analytical proofs that the single-copy
entanglement and the global geometric entanglement of the ground state close to
and at criticality behave as the entanglement entropy. These results are in
deep contrast to what is found in one- dimensional spin systems where these
three entanglement measures behave differently.Comment: 4 pages, 2 figures, published versio
Gutzwiller density functional theory for correlated electron systems
We develop a new density functional theory (DFT) and formalism for correlated
electron systems by taking as reference an interacting electron system that has
a ground state wavefunction which obeys exactly the Gutzwiller approximation
for all one particle operators. The solution of the many electron problem is
mapped onto the self-consistent solution of a set of single particle
Schroedinger equations analogous to standard DFT-LDA calculations.Comment: 4 page
Searching for thermal signatures of persistent currents in normal metal rings
We introduce a calorimetric approach to probe persistent currents in normal
metal rings. The heat capacity of a large ensemble of silver rings is measured
by nanocalorimetry under a varying magnetic field at different temperatures (60
mK, 100 mK and 150 mK). Periodic oscillations versus magnetic field are
detected in the phase signal of the temperature oscillations, though not in the
amplitude (both of them directly linked to the heat capacity). The period of
these oscillations (, with the magnetic flux quantum)
and their evolution with temperature are in agreement with theoretical
predictions. In contrast, the amplitude of the corresponding heat capacity
oscillations (several ) is two orders of magnitude larger than
predicted by theory
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