Hubbard-Stratonovich-like Transformations for Few-Body Interactions

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the analytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three- and more-body interactions, is presented.Comment: Conference proceeding, 8 pages, 4 figure

Sampling General N-Body Interactions with Auxiliary Fields

We present a general auxiliary field transformation which generates effective interactions containing all possible N-body contact terms. The strength of the induced terms can analytically be described in terms of general coefficients associated with the transformation and thus are controllable. This transformation provides a novel way for sampling 3- and 4-body (and higher) contact interactions non-perturbatively in lattice quantum monte-carlo simulations. We show that our method reproduces the exact solution for a two-site quantum mechanical problem.Comment: 5 pages, 1 figure and a supplemental Mathematica noteboo

Some Novel Phenomena at High Density

Astrophysical environments probe matter in ways impossible on Earth. In particular, matter in compact objects are extraordinarily dense. In this thesis we discuss two phenomena that may occur at high density. First, we study toroidal topological solitons called vortons, which can occur in the kaon-condensed color-flavor-locked phase of high-density quark matter, a candidate phase for the core of some neutron stars. We show that vortons have a large radius compared to their thickness if their electrical charge is on the order of 104 times the fundamental charge. We show that shielding of electric fields by electrons dramatically reduces the size of a vorton. Second, we study an unusual phase of degenerate electrons and nonrelativistic Bose-condensed helium nuclei that may exist in helium white dwarfs. We show that this phase supports a previously-unknown gapless mode, known as the half-sound, that radically alters the material's specific heat, and can annihilate into neutrinos. We provide evidence that this neutrino radiation is negligible compared to the star's surface photoemission