Talks

Introduction of the torsion tensor on the space-time manifold  leads to a Weyl invariant geometry, in which t e torsion trace acts as a "U(1)" compensating field for the conformal transformations. Such  symmetry can be extended to the whole matter sector included in the  standard model by coupling the Higgs scalar (and all other possible  fundamental scalars) to the torsion. A relevant question is then whether such framework can be used to describe cosmic inflation, as a spontaneous symmetry breaking phenomenon. It turns out that this is indeed possible because the Weyl invariance imposes a distinct field space geometry, which introduces a slow roll plateau in the otherwise  too steep quartic potential dictated by Weyl symmetry. The model can  have observable consequences that distinguish it from other inflationary scenarios, at least under some choices of initial conditions.

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body ``scar states'' in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at infinite temperature that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact E = 0 states) and open boundary conditions (two E = 0 states and one each E =± √2). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in 1D at infinite temperature. We show that the nearby many-body scar states with energies E ~± 1.33 andE ~ ± 2.66 can be well approximated as ``quasiparticle excitations" on top of our exact E = 0 states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Experiments on organic crystals whose structure is well-described by the two-dimensional triangular lattice have found a lack of magnetic ordering down to the lowest accessible temperatures, indicative of a quantum spin liquid phase; however, the precise nature of this phase remains an open question.  In this talk, I present strong evidence that the triangular lattice Hubbard model at half filling, a physically motivated model of these organic crystals, realizes a chiral spin liquid phase.  In particular, I show that the model has a nonmagnetic insulating phase between a metallic phase for weak interactions and a magnetically ordered phase for strong interactions, and that the intermediate phase exhibits the expected properties of a chiral spin liquid: spontaneous breaking of time-reversal symmetry, topological ground state degeneracy, a quantized spin Hall effect, and characteristic level counting in the entanglement spectrum.  These results were obtained using the infinite-system density matrix renormalization group (iDMRG) method in a mixed real- and momentum-space basis; in the talk, I will also discuss the benefits of this mixed-space approach to DMRG in general, including its applicability to systems such as twisted bilayer graphene for which a large unit cell makes real-space DMRG impractical. 

Hidden sectors are motivated by a range of phenomena unexplained by the Standard Model, such as dark matter, neutrino masses, and the baryon asymmetry. Hidden sector particles below the weak scale can be copiously produced at high-energy and intensity-frontier experiments, but may have evaded detection with current searches.
I will discuss new searches I am doing with the BaBar collaboration that are probing unexplored, well-motivated territory for hidden sectors. I will also show how signatures such as displaced vertices motivate comprehensive, complementary searches at low- and high-energy experiments.

We consider a natural extension of general relativity, by the addition of a term which is a topological invariant when the cosmological constant is in fact constant.  Allowing the cosmological constant to vary, we discover it is endowed with a natural dynamics, which also includes a mechanism to suppress its value.   A key role in hiding the consequences of a dynamical cosmological constant is played by the torsion of the spacetime connection.

As a dynamical variable, the varying cosmological constant turns out to be canonically conjugate to a measure of intrinsic, cosmological time, given by the Chern-Simons invariant of the Ashtekar connection (which we originally studied with Chopin Soo).  As a result, a small quantum universe that "knows what time it is" does not know the value of the cosmological constant, and visa versa.   This leads to some novel scenarios for the early universe.

This is joint work in progress with Stephon Alexander, Joao Magueijo and Robert Sims.