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How to deal with diffeomorphism symmetries is one of the difficult problems in general relativity. Because of the diffeomorphism symmetries, we need to consider diffeomorphism invariant operators and gravitational dressing. In this work, we consider a special gravitational dressing which is to locate the operator by shooting geodesic from the spatial boundary. We try to use Peierls bracket to study the commutator between this gravitational dressing operator and the ADM energy operator. We found the ADM energy increase/decrease when the extra created out-going particle is in front of/behind the event horizon. Our result strengthens the Marolf-Polchinski firewall argument in some sense. In the talk, I will first briefly review the Peierls bracket, which is a linear response interpretation of bracket computation in covariant phase space formalism. We also illustrate the Peierls bracket with several examples. After that, we use Peierls bracket to study the Hamiltonian flow of the gravitational dressing operator, from which we can read out the commutator between the gravitational dressing operator with the ADM energy operator.

The entanglement pattern of a quantum many-body system can be characterized by quasiparticles and emergent gauge fields, much like those found in Maxwell's theory. My talk begins with the basic aspects of symmetry fractionalization and emergent gauge fields in strongly correlated systems. I will further extend this paradigm into a new type of quantum many-body state, dubbed "fracton phase," from a quantum melting transition of plaquette paramagnetic crystals. These exotic states contain fractionalized sub-dimensional quasiparticles with constraint motion and emergent higher-rank gauge fields. Such constraint dynamics of the quasiparticles bring about an intriguing Bose metal phase with quasi-long range order and yields non-local quantum entanglement. In particular, the key peculiarities of this phase is the UV/IR mixing, where the short wavelength physics controls the low energy theory and hence challenges the standard notion of the renormalization group perspective.

If time is described by a fundamental process rather than a coordinate, it

interacts with any physical system that evolves in time. The resulting
dynamics has recently been shown to be consistent provided the fundamental
period of the time system is sufficiently small. A strong upper bound T_C
< 10^{-33}s of the fundamental period of time, several orders of magnitude
below any direct time measurement, can be obtained from bounds on
dynamical variations of the period of a lab system evolving in time.
Possible cosmological implications will be discussed.

Two of the dominant channels to produce black-hole binary mergers are believed to be the isolated evolution of stellar binaries in the field and dynamical formation in star clusters. Pair instabilities prevent stellar collapse from generating black holes more massive than about 45-60 solar mass. This  “mass gap” only applies to the field formation scenario: repeated mergers in clusters can fill the gap. A similar reasoning applies to the binary’s spin parameters. If black holes are born slowly rotating, the high-spin portion of the parameter space (the “spin gap”) can only be filled by black-hole binaries that are assembled dynamically. I will discuss how such signatures are a smoking gun for the hierarchical origin, and how recent detections (GW190521 and GW190412) fit in this context. I will also talk about how we may be able to reconstruct the properties of progenitors of second-generation black holes.

Walgate and Scott have determined the maximum number of generic pure quantum states in multipartite space that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine this number in a more general setting in which the local parties have access to pre-shared entanglement in the form of a resource state. We find that, for an arbitrary pure resource state, this number is equal to the Krull dimension of (the closure of) the set of pure states obtainable from the resource state by SLOCC. This dimension is known for several resource states, for example the GHZ state.

Local state discrimination is closely related to the topic of entangled subspaces, which we study in its own right. We introduce r-entangled subspaces, which naturally generalize previously studied spaces to higher multipartite entanglement. We use algebraic geometric methods to determine the maximum dimension of an r-entangled subspace, and present novel explicit constructions of such spaces. We obtain similar results for symmetric and antisymmetric r-entangled subspaces, which correspond to entangled subspaces of bosonic and fermionic systems, respectively.

A planar map is a canonical model for a discrete surface which is studied in probability theory, combinatorics, theoretical physics, and geometry. Liouville quantum gravity provides a natural model for a continuum random surface with roots in string theory and conformal field theory. After introducing these objects, I will present a joint work with Xin Sun where we prove convergence of random planar maps to a Liouville quantum gravity surface under a discrete conformal embedding which we call the Cardy embedding.

In this talk I will discuss the universal properties of thermal transport in conformal field theories that are perturbed by a TTbar operator. TTbar-deformation is known to be an exactly solvable deformation in that the spectrum of the undeformed theory alone suffices to predict that of the deformed theory. Unique properties of TTbar deformation allow us to study the TTbar-deformed CFTs using two disparate methods: integrability and holography. I will apply these two approaches to study the non-equilibrium steady states and Drude weights, finding perfect agreement. I will also explain how the integrability-based approach yields the exact momentum diffusion constant, which, to our surprise, also happens to satisfy a universal formula. Finally I will briefly touch upon a curious connection between TTbar-deformed CFTs and an integrable cellular automaton model called the Rule 54 chain.

The discovery of astrophysical gravitational waves has opened a new avenue to explore the cosmos using transients. I will discuss a few new frontiers in the field of physical cosmology and fundamental physics that can be explored using gravitational waves from the current generation gravitational wave detectors such as LIGO/Virgo, and in the future from gravitational wave detectors such as LISA, Einstein Telescope, and Cosmic Explorer. I will elucidate the existence of synergies between electromagnetic probes and gravitational wave probes and their importance in understanding the standard model of cosmology and unveiling new physics.

Metals are ubiquitous in nature. One would like to determine the effective field theory that describe the low-energy physics of a metal. Many materials are successfully described by the so-called "Fermi liquid theory", but there is also much interest in "non-Fermi liquid metals" that evade such a description.

In this talk, I will present a very general perspective on metals that strongly constrains the possible effective field theories. The discussion is based on powerful theoretical concepts such as emergent symmetries and anomalies. From this perspective, combined with experimental observations, one can derive strong and unexpected conclusions about the nature of a particular kind of non-Fermi liquid metal, the "strange metal" observed in doped cuprates.

In this talk, I argue that the question of whether a physical system can be simulated on a computer is important not just from a practical perspective but also a fundamental one. We consider the complexity of simulating Hamiltonians with respect to both dynamics and equilibrium properties. This gives us a classification and a phase diagram of the complexity.  I will cover recent results in this topic, such as a dynamical complexity phase diagram for a long-range bosonic Hamiltonian and a complexity classification of the local Hamiltonian problem in the presence of a spectral gap. I will talk about the physical implications of these results and cover some of the basic proof ideas if time permits.

While spacetime and quantum theory are crucial parts of modern theoretical physics, the problem of quantum gravity demonstrates that their full relationship is not yet completely understood. In my talk, I report on two recent results that aim to shed light on this relationship via ideas and tools from quantum foundations.

We start with the setting of (semi-) device-independent quantum information protocols. In this scenario one considers abstract black boxes that are characterised by their input-output statistics. Typically, these inputs and outputs are assumed to be abstract labels from a finite set of integers. We replace the abstract inputs with physical inputs that correspond to continuous spatio-temporal degrees of freedom, e.g. angles of polarisers and time-durations of laser pulses. This framework gives new insights about the relation between space, time, and quantum correlations, and it gives rise to new kinds of Bell non-locality witnesses.

We then turn to the topic of quantum reference frames. Specifically, we consider a composite quantum system and an outside experimenter who does not have access to an external reference frame to specify all of the system's properties. We show that for such an observer the possible descriptions of states and observables are related by quantum reference frame transformations that have been independently proposed in recent works. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and we introduce a relational generalisation of the partial trace that applies to such situations.