Talks

It is well-known that sufficiently strong interactions can destabilize some SPT phases of free fermions, while others remain stable even in the presence of interactions. It is also known that certain interacting phases cannot be realized by free fermions. In this talk, we will study both of these phenomena in low dimensions and determine the map from free to interacting SPT phases for an arbitrary unitary symmetry. We will also describe how to compute invariants characterizing interacting phases for free band Hamiltonians with symmetry (in any dimension) using only representation theory.

I will discuss how holographic and effective field theory methods could shed light on important open questions in low energy condensed matter systems. I will focus on the study of the vibrational degrees of freedom, i.e. ''phonons'', in liquids, solids and disordered systems like glasses. Building intuition from the holographic systems I will tackle the problem of the low frequency elastic response in liquids and the universal emergence of the boson peak in ordered crystals and amorphous solids.

Laser spectroscopy of muonic hydrogen [1,2] yielded a proton rms charge radius which is 4% (or ~6 sigmas) smaller than the CODATA value [3]. This discrepancy is now called the "proton radius puzzle" [4].
Also the deuteron charge radius from muonic deuterium [5] is 6 sigmas smaller than the
CODATA value, but consistent with the smaller proton inside the deuteron.
These smaller charge radii, when combined with precision measurements of the 1S-2S transitions in regular (electronic) hydrogen [6] and deuterium [7], yield a 6 sigmas smaller value of the Rydberg constant [8], compared to the CODATA value.
In this talk I will report about a new measurement of the Rydberg constant from the 2S-4P transition in regular hydrogen performed in Garching [9], which supports the smaller, "muonic" value. More recently, however, a new measurement of the 1S-3S transition in Paris confirmed the larger proton radius [10].
Several new measurements, such as hydrogen from Toronto, elastic electron scattering at lower Q², and new results from electronic and muonic helium will help understand the proton radius puzzle.

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.