Quantum and Gravitational Theory Group

August 30, 2021

September 6, 2021

September 13, 2021

"Emergent criticality in non-unitary random dynamics"

We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends toward steady states with logarithmic violations of the entanglement area law and power law correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a spacelike time direction. We argue that this behavior is generic in non-unitary free quantum dynamics with time-dependent randomness, and we show that the emergent conformal dynamics of two-point functions arises out of a simple “nonlinear master equation.” In addition, we construct solvable quadratic Sachdev-Ye-Kitaev chains with non-unitary dynamics in the large N limit and we argue the emergent conformal field theory is due to the existence of the Goldstone modes in the enlarged replica space.

September 20, 2021

"Phase transition in von Neumann entanglement entropy from replica symmetry breaking"

We study the entanglement transition in monitored Brownian SYK chains in the large-N limit. Without measurement the steady state n-th Renyi entropy is obtained by summing over a class of solutions, and is found to saturate to the Page value in the $n \rightarrow 1$ limit. In the presence of measurements, the analytical continuation $n \rightarrow 1$ is performed using the cyclic symmetric solution. The result shows that as the monitoring rate increases, a continuous von Neumann entanglement entropy transition from volume-law to area-law occurs at the point of replica symmetry unbreaking.

September 27, 2021

October 4, 2021

"Negativity in random tensor networks and holography"

We will discuss mixed state entanglement in random tensor networks, using the notion of negativity. Tensor networks are useful in many-body physics, as well as in holography, particularly in fixed-area states. We find the negativity spectrum, which is the analog of entanglement spectrum, in a general random tensor network with large bond dimensions, using a related flow network problem. We also study mixed states of a system coupled to gravity, such as a black hole with its Hawking radiation. We find island contributions in such systems, and show the Euclidean wormhole origin of these contributions in a Jackiw-Teitelboim gravity model.

October 11, 2021

"Confinement and Flux Attachment"

Flux-attached gauge theories are a novel class of lattice gauge theories whose gauge constraints involve both electric and magnetic operators. Like ordinary gauge theories, they possess confining phases. Unlike ordinary gauge theories, their confinement does not imply a trivial gapped vacuum. Instead, the confining phases subtly straddle a boundary between topological and trivial phases. I will describe some salient properties of these phases for different choices of flux attachment. In particular, I will demonstrate a simple example of a gapped, local theory whose topological entanglement entropy is positive (i.e. whose total quantum dimension is less than one).

October 19, 2021

*Please note that this seminar takes place at a non-standard time of 10:30am on a Tuesday

"Large Scale Structure from Microphysics"

In this talk, I will describe my efforts to understand the nature of the mysterious dark matter. I provide an overview of the general problem and then describe my current approach to it, which is to characterize the behavior of a proposed dark matter particle, the axion. I will give some insight into how I am using a range of tools -- model building, computation, and neutron stars -- to get at the basic question of “what is the statistical mechanics of axion dark matter?” I will discuss work that shows that the self-interaction should not be ignored and that the sign of the interaction makes a significant difference in the evolution of the system, both for QCD axions and fuzzy dark matter.

October 25, 2021

"Analyticity and Unitarity for Cosmological Correlators"

Based on https://arxiv.org/abs/2108.01695. I will consider quantum field theory on a rigid de Sitter space. I will first discuss how the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. I will use this to explain the analytic structure of the spectral density that characterize a late-time four-point function. Then I will discuss a positivity condition that encodes the unitarity of the time evolution in the bulk de Sitter space. If time permits I will discuss some concrete examples in perturbation theory that illustrate these properties.

November 1, 2021

"Algebra of diffeomorphism invariant observables in Jackiw-Teitelboim gravity"

Diffeomorphism symmetry is an intrinsic difficulty in gravitational theory, which appears in almost all of the questions in gravity. As is well known, the diffeomorphism symmetries in gravity should be interpreted as gauge symmetries, so only diffeomorphism invariant operators are physically interesting. However, because of the non-linear effect of gravitational theory, the results for diffeomorphism invariant operators are very limited.

In this work, we focus on the Jackiw-Teitelboim gravity in classical limit, and use Peierls bracket (which is a linear response like computation of observables’ bracket) to compute the algebra of a large class of diffeomorphism invariant observables. With this algebra, we can reproduce some recent results in Jackiw-Teitelboim gravity including: traversable wormhole, scrambling effect, and SL(2) charges. We can also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the “typical state” version of the firewall paradox.

In the talk, I will first give a brief introduction of Peierls bracket, and then use the Peierls bracket to study the brackets between diffeomorphism invariant observables in Jackiw-Teitelboim gravity. I will then give two applications of this algebra: reproducing the scrambling effect, and studying the energy change after creating an excitation in the bulk.

Reference: 2108.04841

November 8, 2021

"Amplitudes and the Riemann Zeta Function"

In this talk, I will connect physical properties of scattering amplitudes to the Riemann zeta function. Specifically, I will construct a closed-form amplitude, describing the tree-level exchange of a tower with masses \(m^2_n = \mu^2_n\), where \(\zeta(\frac{1}{2}\pm i \mu_n) = 0\). Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of \(\zeta\). Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of \(1/\mu^2_n\).

November 15, 2021

"Free fermions and parafermions"

Free fermions are ubiquitous in theoretical physics. Typically such models are found by expressing the Hamiltonian and/or action as a sum or integral over bilinears of local fermionic operators or fields, sometimes requiring a Jordan-Wigner transformation. I describe models that become free fermionic only after under a much subtler transformation that is both non-local and non-linear in the original interacting fermions. Including also the usual fermion bilinears breaks the solvability but allows a simple lattice analog of an interacting conformal field theory, very useful for numerical analysis. I will also give a brief overview of how free-parafermion chains can be solved in a similar fashion.

November 22, 2021

"Black hole microstate statistics from Euclidean wormholes"

Over the last several years, it has been shown that black hole microstate level statistics in various models of 2D gravity are encoded in wormhole amplitudes. These statistics quantitatively agree with predictions of random matrix theory for chaotic quantum systems; this behavior is realized since the 2D theories in question are dual to matrix models. But what about black hole microstate statistics for Einstein gravity in 3D and higher spacetime dimensions, and ultimately in non-perturbative string theory? We will discuss progress in these directions. In 3D, we compute a wormhole amplitude that encodes the energy level statistics of BTZ black holes. In 4D and higher, we find analogous wormholes which appear to encode the level statistics of black holes. Finally, we study analogous Euclidean wormholes in the low-energy limit of type IIB string theory; we provide evidence that they encode the level statistics of black holes in AdS5 x S5. Remarkably, these wormholes appear to be stable in appropriate regimes, and dominate over brane-anti-brane nucleation processes in the computation of black hole microstate statistics.

November 29, 2021

"An introduction to hyperthreads"

Bit threads, a dual description of the Ryu-Takayanagi formula for holographic entanglement entropy (EE), can be interpreted as a distillation of the quantum information to a collection of bell pair between different boundary regions. In this talk I will discuss a generalization to hyperthreads which can connect more than two boundary regions leading to a rich and diverse class of convex programs. By modeling the contributions of different species of hyperthreads to the EE’s of simple multipartite states (namely GHZ and perfect tensors) I will argue that this framework may be useful for helping us to begin to probe the multipartite entanglement of holographic systems. Furthermore, I will demonstrate how this technology can potentially be used to understand or possibly prove entropy cone inequalities and may provide an avenue to address issues of locking.

December 2, 2021

*Please note that this seminar takes place at a non-standard time of 11:45am on a Thursday

"Quantum minimal surfaces from quantum error correction"

In 2016 Harlow taught us that we can understand the Ryu-Takayanagi formula as a feature of quantum error correction. This explained how we should think about both the entanglement wedge and the area term in the formula. However, his analysis only applied in the special case of small code subspaces, in which the entanglement wedge is the same for all states. I'm going to tell you about my recent work with Geoff Penington, in which we generalize this story to arbitrarily large code subspaces. Moreover, we derive that the entanglement wedge should minimize the area plus entropy of bulk fields. This involves defining the entanglement wedge via a new kind of quantum error correcting code, reducing to Harlow's in the appropriate special case. This also naturally leads to a precise quantum information theoretic definition of the area of bulk surfaces. Based on https://arxiv.org/abs/2109.14618.