Quantum and Gravitational Theory Group

August 23, 2022

"Entanglement entropy and the lattice-continuum correspondence"

Entanglement entropy (EE) is notoriously tricky (or impossible) to rigorously define in quantum field theory. However, EE is straightforward to define in a finite-dimensional quantum system. The recent progress in understanding the correspondence between lattice and continuum theories now makes it possible to define and study EE in continuum theories via finite, lattice-based quantities. I will explain how this works and how two interesting lessons emerge. One is that the divergences associated to the EE in continuum theories are not governed by the smallest UV scale (the lattice spacing) but rather by a much larger scale (the "smoothing length"). The second is that the Reeh-Schlieder theorem can be formulated in the context of lattice theories, with the smoothing length once again playing a key role in determining its breakdown.

*** Note: room and time change, seminar held at 11:10am in Abelson 229 ***

August 30, 2022

"NLTS Hamiltonians from good quantum codes"

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). Our recent work https://arxiv.org/abs/2206.13228 (with Nikolas Breuckmann and Chinmay Nirkhe) proves this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians. This talk will provide background on the conjecture, its relevance to quantum many-body physics and quantum complexity theory, and touch upon the proof techniques.

September 6, 2022

"Light-ray moments as endpoint contributions to modular Hamiltonians"

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J of modular weight n over a space-like surface. We show that the modular Hamiltonian with respect to the excited state and the Rindler subregion has a contribution associated with the entangling surface, which has the form of a sum of light-ray moments of the perturbing operator J and its descendants. This endpoint contribution is sensitive to the details of the perturbation near the entangling surface, including the shape of the space-like surface. For perturbations on null planes only moments of J itself appear in the endpoint contribution.

September 13, 2022

"The connected wedge theorem and its consequences"

I will discuss new work with Alex May and Beni Yoshida that elaborates the connection between bulk causal structure and boundary entanglement in AdS/CFT. The key result is a new theorem showing that certain complicated bulk causal structures must be supported by an associated pattern of large-N bipartite boundary entanglement. I will also explain how this gravity-oriented program has taught us new things about quantum information theory that have implications for non-gravitational physics.

September 20, 2022

"Large N Matrix Quantum Mechanics as a Quantum Memory"

We explore the possibility of building a quantum memory that is robust to thermal noise using large N matrix quantum mechanics models. First, we investigate the gauged SU(N) matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, Tc, below which the encoded quantum information is protected from thermal noise for a memory time scaling as N^2. Conversely, for temperatures higher than Tc, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number N^2 of qubits, with interactions derived from an approximate SU(N) symmetry. In both ungauged models, we find that the effects of gauging can be mimiced using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.

September 27, 2022

October 4, 2022

"The Penrose Inequality as a Constraint on Low Energy Quantum Gravity"

In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible with AdS/CFT. It is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. In the case where the dominant energy condition holds, a proof of the PI for spherical, planar or hyperbolic symmetry is given. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).

October 11, 2022

"Comments on hunting the graviton"

Detecting “a graviton” is an obviously interesting goal, if it is possible. Dyson has given some compelling arguments that this might be impossible. I’ll review his arguments and suggest two possible alternatives. One is that it may be possible to detect entanglement generated between mesoscopic objects through their gravitational interactions; I’ll review some proposals for this and discuss to what extent this is related to the existence of gravitons. The other is a more direct counter example to Dyson’s argument, using certain axion detector architectures repurposed as graviton detectors.

October 18, 2022

October 25, 2022

November 1, 2022

November 8, 2022

November 15, 2022

November 22, 2022

November 29, 2022

December 6, 2022