Scientific Series

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension ≥ 2.

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size, without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional onsite symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D `cluster state' model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally. Joint work with Stephen Bartlett.

The strong interaction of quarks and gluons is described theoretically within the framework of Quantum Chromodynamics (QCD). The most promising way to evaluate QCD for all energy ranges is to formulate the theory on a 4-dimensional Euclidean space-time grid, which allows for numerical simulations on state of the art supercomputers. We will review the status of lattice QCD calculations providing examples such as the hadron spectrum and the inner structure of nucleons. We will then point to problems that cannot be solved by conventional Monte Carlo simulation techniques, i.e. non-zero baryon density, the matter-antimatter asymmetry and real time simulations. It will be demonstrated at the example of the 1+1 dimensional Schwinger model that tensor network techniques are able to overcome these problems showing that with this approach --and eventual quantum simulations-- a path for solving QCD is opening up.

The ultra-strong magnetic fields of magnetars have profound implications for their radiative phenomena. We studied the dynamics of strong magnetic fields inside and outside magnetars. Inside the magnetar, the strong magnetic stress can break the crust and trigger plastic failures. The interaction between magnetic fields and plastic failures is studied in two scenarios: 1. Internal Hall waves launched from the core-crust interface can initiate plastic failures and lead to X-ray outbursts. 2. External Alfven waves produced by giant flares can also initiate crustal plastic failures which dissipate the waves and give rise to delayed thermal afterglow. The crustal dissipation of Alfven waves is competed by the magnetospheric dissipation outside the magnetar. Using a high order simulation of Force-Free Electrodynamics (FFE), we found that the magnetospheric dissipation of Alfven waves is generally slow and most wave energy will dissipate inside the magnetar.

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. 

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.