Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems

I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped, one-dimensional system. I show that the edge exponent in the probability density function of the work is insensitive to the presence of interactions and can take only one of three values: +1/2, -1/2 and -3/2. It also turns out that there is an interesting interplay between spontaneous symmetry breaking or the presence of bound states and the exponents. For instantaneous global protocols, I find that the presence of the one-particle channel creates dynamical phase transitions in the time evolution.

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $kgg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $lambda$. Moreover for $lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.