Path dependent scaling of geometric phase near a quantum multi-critical point

We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle $\eta$. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points `quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter $\alpha$ that defines a path, upto a critical value $\alpha = \alpha_{c}=2$. For $\alpha > \alpha_{c}$, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.Comment: 5 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

Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench in the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g. by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder