8 research outputs found
Quantum quenches from integrability: the fermionic pairing model
Understanding the non-equilibrium dynamics of extended quantum systems after
the trigger of a sudden, global perturbation (quench) represents a daunting
challenge, especially in the presence of interactions. The main difficulties
stem from both the vanishing time scale of the quench event, which can thus
create arbitrarily high energy modes, and its non-local nature, which curtails
the utility of local excitation bases. We here show that nonperturbative
methods based on integrability can prove sufficiently powerful to completely
characterize quantum quenches: we illustrate this using a model of fermions
with pairing interactions (Richardson's model). The effects of simple (and
multiple) quenches on the dynamics of various important observables are
discussed. Many of the features we find are expected to be universal to all
kinds of quench situations in atomic physics and condensed matter.Comment: 10 pages, 7 figure
One-particle dynamical correlations in the one-dimensional Bose gas
The momentum- and frequency-dependent one-body correlation function of the
one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive
regime is studied using the Algebraic Bethe Ansatz and numerics. We first
provide a determinant representation for the field form factor which is
well-adapted to numerical evaluation. The correlation function is then
reconstructed to high accuracy for systems with finite but large numbers of
particles, for a wide range of values of the interaction parameter. Our results
are extensively discussed, in particular their specialization to the static
case.Comment: 19 Pages, 7 figure
Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model)
is investigated with techniques based on the integrability of the system.
Combining a knowledge of particle quasi-momenta to exponential precision in the
system size with determinant representations of matrix elements of local
operators coming from the Algebraic Bethe Ansatz, we obtain rather general
analytical results for the zero-temperature dynamical correlation functions of
the density and field operators. Our results thus provide quantitative
predictions for possible future experiments in atomic gases or optical
waveguides.Comment: 26 pages, 5 figure
Entanglement entropy of excited states
We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling
Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditions
Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the 1D integrable Lieb-Liniger model of interacting bosons. For flat initial conditions, it requires the knowledge of the overlap between the uniform state and arbitrary exact Bethe eigenstates. The same quantity is also central in the study of the quantum quench from a 1D non-interacting Bose-Einstein condensate upon turning interactions. We compare recent advances in both domains, i.e. our previous exact solution, and a new conjecture by De Nardis et al. This leads to new exact results and conjectures for both the quantum quench and the KPZ problem
Correlation Functions of the Open XXZ Chain II.
38 pagesInternational audienceWe derive compact multiple integral formulas for several physical spin correlation functions in the semi-infinite XXZ chain with a longitudinal boundary magnetic field. Our formulas follow from several effective re-summations of the multiple integral representation for the elementary blocks obtained in our previous article (I). In the free fermion point we compute the local magnetization as well as the density of energy profiles. These quantities, in addition to their bulk behavior, exhibit Friedel type oscillations induced by the boundary; their amplitudes depend on the boundary magnetic field and decay algebraically in terms of the distance to the boundary