Jorn Mossel

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 with models fulfilling the proposed criteria.

Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the one-dimensional 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.

Generalized TBA and generalized Gibbs

We consider the extension of the thermodynamic Bethe Ansatz 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 provided simple requirements are met. We show how a knowledge of the saddle-point rapidity distribution is equivalent to that of all generalized inverse temperatures and how the standard equilibrium equations for e.g. excitations are simply generalized.

Relaxation dynamics in the gapped XXZ spin-1/2 chain

We study the dynamics of a quench-prepared domain wall state released into a system whose unitary time evolution is dictated by the Hamiltonian of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Using exact wavefunctions and their overlaps with the domain wall state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime (Δ>1) cannot thermalize in the strict sense.

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 (Δ>1). 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 π/2-momentum line, its overall anisotropy dependence, and its contribution to sum rules.

The spin-exchange dynamical structure factor of the S=1/2 Heisenberg

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.

Adjacent spin operator dynamical structure factor of the S = 1/2 Heisenberg chain

Considering the adjacent spin operators

Remarks on the notion of quantum

S^z_jS^z_{j+1}

Spin-Exchange Dynamical Structure Factor of the S=1/2 Heisenberg Chain

and

Geometric quenches in quantum integrable systems

S^-_jS^-_{j+1}