Condensed Matter Theory

Abstract:

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

Abstract:

For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random sampling of inputs than complex outputs are. Here, we derive probability bounds that are based on the complexities of the inputs as well as the outputs, rather than just on the complexities of the outputs. The more that outputs deviate from the coding theorem bound, the lower the complexity of their inputs. Since the number of low complexity inputs is limited, this behaviour leads to an effective lower bound on the probability. Our new bounds are tested for an RNA sequence to structure map, a finite state transducer and a perceptron. The success of these new methods opens avenues for AIT to be more widely used.

Abstract:

Nodal semimetals are a unique platform to explore topological signatures of the unusual band structure that can manifest by accumulating a nontrivial phase in quantum oscillations. Here we report a study of the de Haas–van Alphen oscillations of the candidate topological nodal line semimetal CaAgAs using torque measurements in magnetic fields up to 45 T. Our results are compared with calculations for a toroidal Fermi surface originating from the nodal ring. We find evidence of a nontrivial π phase shift only in one of the oscillatory frequencies. We interpret this as a Berry phase arising from the semiclassical electronic Landau orbit which links with the nodal ring when the magnetic field lies in the mirror (ab) plane. Furthermore, additional Berry phase accumulates while rotating the magnetic field for the second orbit in the same orientation which does not link with the nodal ring. These effects are expected in CaAgAs due to the lack of inversion symmetry. Our study experimentally demonstrates that CaAgAs is an ideal platform for exploring the physics of nodal line semimetals and our approach can be extended to other materials in which trivial and nontrivial oscillations are present.