Chaos in a deformed Dicke model

The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion onlyat one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincar ́e sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relationwith an additional conserved quantity that the model can exhibit.

Neutron Oscillations and the Parity Doubling Theorem

We review several aspects of parity and CP violation in the framework of neutron-antineutron oscillations. We focus on the parity doubling theorem, which provides a criterion for neutron oscillation in the general theory with ΔB=2 baryon number-violating interactions. We prove by explicit calculations that the violation of the conventional parity symmetry with P2=1 is the necessary condition for neutron oscillations to happen. While the CP violation is not manifest in the oscillation, it is nevertheless intrinsic to the system, and it is transferred, by the mixing matrix, to the neutron interactions and potentially observable as a contribution to the electric dipole moment.

Gauging the Kitaev chain

We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.

Lorentz invariance of basis tensor gauge theory

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.