Spontaneous symmetry breaking and frustrated phases.

We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen so as to produce frustration. At zero temperature, this system undergoes several quantum phase transitions from both gapped to gapless and gapless to gapless phases, providing a very rich phase structure with disordered, homogeneous, and modulated ordered phases meeting in a quantum Lifshitz point. The gapless phases spontaneously break spatial lattice translations as well as internal symmetries of the form U(1)^{N_{c}}, where N_{c} is the number of independent pitch vectors that arise in the homogeneous and modulated ordered phases. We carry out a detailed analysis of the quantum critical behavior, discussing the mechanism leading to the phase transitions. We also discuss a proper characterization of all the gapless phases as well as the nature of the Goldstone excitations. We study the behavior of the correlation functions and identify regions in the phase diagram where the system exhibits generalized symmetries such as polynomial shift symmetry. This type of symmetry plays an important role in the so-called fractonic phase, which is an exotic form of matter recently discovered.

Duality Between 3D Massive Thirring and Maxwell-Chern-Simons Models from 2D Bosonization.

Bosonization techniques are important nonperturbative tools in quantum field theory. In three dimensions they possess interesting connections to topologically ordered systems and ultimately have driven the observation of an impressive web of dualities. In this work, we use the quantum wires formalism to show how the fermion-boson mapping relating the low-energy regime of the massive Thirring model in three spacetime dimensions with the Maxwell-Chern-Simons model can be obtained from the exact bosonization in two dimensions.

Supersymmetric extension of the quantum spherical model.

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.