Talks

It is well known that the ground state energy of many-particle Hamiltonians involving only 2- body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are 'N-representable' is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

What lies beyond the Standard Model of particle physics? Are there very weakly interacting forms of matter and forces waiting to be discovered? In this talk I will describe some of the efforts underway to detect very weakly interacting particles, from dark matter to new forces. I will discuss recent observations and their theoretical significance as well as the connection to other experimental results. I will conclude with a short summary of the different frontiers and their interrelations.

Traditional condensed matter physics is based on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Mean-field theory is a powerful method to describe symmetry breaking phases and phase transitions by assuming the ground state wavefunctions for many-body systems can be approximately described by direct product states. The Fermi liquid theory is another powerful method to study electron systems by assuming that the ground state wavefunctions for the electrons can be approximately described by Slater determinants. From the encoding point of view, both methods only use a polynomial amount of information to approximately encode many-body ground state wavefunctions which contain an exponentially large amount of information. Moreover, another nice property of both approaches is that all the physical quantities (energy, correlation functions, etc.) can be efficiently calculated (polynomially hard). In this talk, I'll introduce a new class of states: (Grassmann-number) tensor-net states. These states only need polynomial amount of information to approximately encode many-body ground states. Many classes of states, such as Slater determinant states, projective states, string-net states and their generalizations, etc., are subclasses of (Grassmann-number) tensor-net states. However, calculating the physical quantities for these state can be exponentially hard in general. To solve this difficulty, we develop the Tensor-Entanglement Renormalization Group (TERG) method to efficiently calculate the physical quantities. We demonstrate our algorithm by studying several interesting boson/fermion models, including t-J model on a honeycomb lattice.

The availability of high precision observational data in cosmology means that it is possible to go beyond simple descriptions of cosmic inflation in which the expansion is driven by a single scalar field. One set of models of particular interest involve the Dirac-Born-Infeld (DBI) action, arising in string cosmology, in which the dynamics of the field are affected by a speed limit in a manner akin to special relativity. In this talk, I will introduce a scalar-tensor theory in which the matter component is a field with a DBI action. Transforming to the Einstein frame, I will explore the effect of the resulting coupling on the background dynamics of the fields and the first-order perturbations. The coupling forces the scalar field into the minimum of its effective potential, so the dynamics are determined by the DBI field, which has the interesting effect of increasing the number of efolds of inflation and decreasing the boost factor of the DBI field. Focusing on this case, I will show that the power spectrum of the primordial perturbations is determined by the behaviour of the perturbations of the modified DBI field and calculate the effect of varying the model parameters on the inflationary observables.