7 research outputs found
Generalized TBA and generalized Gibbs
We consider the extension of the thermodynamic Bethe Ansatz (TBA) to cases in
which additional terms involving higher conserved charges are added to the
Hamiltonian, or in which a distinction is made between the Hamiltonian used for
time evolution and that used for defining the density matrix. Writing down
equations describing the saddle-point (pseudo-equilibrium) state of the
infinite system, we prove the existence and uniqueness of solutions for
Lieb-Liniger provided simple requirements are met. We show how a knowledge of
the saddle-point rapidity distribution is equivalent to that of all generalized
chemical potentials, and how the standard equilibrium equations for e.g.
excitations are simply generalized.Comment: 9 pages, no figure
Geometric quenches in quantum integrable systems
We consider the generic problem of suddenly changing the geometry of an
integrable, one-dimensional many-body quantum system. We show how the physics
of an initial quantum state released into a bigger system can be completely
described within the framework of the Algebraic Bethe Ansatz, by providing an
exact decomposition of the initial state into the eigenstate basis of the
system after such a geometric quench. Our results, applicable to a large class
of models including the Lieb-Liniger gas and Heisenberg spin chains, thus offer
a reliable framework for the calculation of time-dependent expectation values
and correlations in this nonequilibrium situation.Comment: 8 page
Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
We consider the non-equilibrium dynamics of the interacting Lieb-Liniger gas
after instantaneously switching the interactions off. The subsequent time
evolution of the space- and time-dependent correlation functions is computed
exactly. Different relaxation behavior is observed for different correlation
functions. The long time average is compared with the predictions of several
statistical ensembles. The generalized Gibbs ensemble restricted to a fixed
number of particles is shown to give correct results at large times for all
length scales.Comment: 9 pages, 11 figure
The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
We consider the transverse dynamical structure factor of the anisotropic
Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime
(). Specializing to the case of zero field, we use two independent
approaches based on integrability (one valid for finite size, the other for the
infinite lattice) to obtain the exact two-spinon part of this correlator. We
discuss in particular its asymmetry with respect to the momentum line,
its overall anisotropy dependence, and its contribution to sum rules.Comment: 19 pages, 6 figure
Remarks on the notion of quantum integrability
We discuss the notion of integrability in quantum mechanics. Starting from a
review of some definitions commonly used in the literature, we propose a
different set of criteria, leading to a classification of models in terms of
different integrability classes. We end by highlighting some of the expected
physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2