Quantum Dynamical Applications of Lie Algebra Representations

Germano Resconi, Peter J. Marcer

A. O. BARUT

Stoimen Stoimenov, Malte Henkel

The ageing Lie algebra and especially its local representations for a dynamical exponent z = 2 have played an important role in the description of systems undergoing simple ageing, after a quench from a disordered state to the low-temperature phase. Here, the construction of representations of for generic values of z is described for any space dimension d > 1, generalizing upon earlier results for d = 1. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher order differential operators or the Riesz fractional derivative. Co-variant two-time response functions are derived. Some simple applications to the exactly solvable models of phase separation or interface growth with conserved dynamics are discussed.

Kieran Bull, Jean-Yves Desaules, Zlatko Papić

Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium. An example of such nonthermalizing behavior is the phenomenon of quantum many-body scars, which has been experimentally observed in Rydberg-atom quantum simulators. Here, the authors show that many-body scars can generally be viewed as forming approximate subspaces of ``broken'' Lie algebra representations. Furthermore, they use an iterative process to identify perturbations which ``correct'' the broken Lie algebra, resulting in improved quantum revivals from special initial states. The description of embedded Lie algebra representations unifies several theoretical models, which feature exact many-body scars, with experimentally realized models, such as the constrained Rydberg-atom system, where scars only form an approximate Lie algebra representation.

Róbert Hermann

B.G. Adams, J. Cizek, Josef Paldus