Fusion Rule Measurement in a Topological Qubit
2024-04-19 10:00 - 11:30 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Chetan Nayak, Microsoft and UCSB
Title: Fusion Rule Measurement in a Topological Qubit

What Observables are Safe to Calculate?
2024-04-26 10:30 - 12:00
Quantum Matter in Mathematics and Physics Seminar
Speaker: Jesse Thaler, MIT
Title: What Observables are Safe to Calculate?
Abstract: In collider physics, perturbative quantum field theory is the workhorse framework for computing theoretical predictions to compare to experimental measurements. An observable is called “safe” if its cross section can be predicted order-by-order in perturbation theory with controlled non-perturbative corrections. In this talk, I show that naive definitions of “safety” are inadequate to determine which observable are perturbatively calculable. I then argue for a more refined definition of safety based on principles from optimal transport theory.

From quantum Hall to Hubbard physics in twisted bilayer graphene
2024-05-10 10:00 - 11:30
Quantum Matter in Mathematics and Physics Seminar
Speaker: Eslam Khalaf (Harvard)
Title: From quantum Hall to Hubbard physics in twisted bilayer graphene

Abstract: Early on it was noticed that twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: Hubbard physics and quantum Hall physics. On the one hand, TBG hosts flat topological Landau-level-like bands which realize quantum anomalous Hall states and orbital ferromagnetism under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show experimental signs of fluctuating magnetism, and unconventional superconductivty; all characteristics of Hubbard-model-like physics. The emergence of fluctuating moments is particularly surprising, as localized Wannier states do not exist in topological bands. I will discuss a phenomenological model for the flat bands in TBG that centers the concentration of charge density and, relatedly, the concentration of Berry flux. The bands obtained have excellent quantitative agreement with the Bistritzer-Macdonald model for realistic parameters. I will show that, rather remarkably, the model hosts decoupled flavor moments which despite being only power-law delocalized with infinite localization length, have parametrically small overlap with each other. I will show how this unifies many of the observations in TBG and leads to a novel Mott semimetal phase for intermediate temperatures where moments are thermally disordered but charge fluctuations are mostly frozen.

Improving Mean-Field Theory for Quantum Magnets
2024-05-13 13:30 - 14:30
Quantum Matter in Mathematics and Physics Seminar
Speaker: Junyi Zhang, Johns Hopkins University
Title: Improving Mean-Field Theory for Quantum Magnets
Abstract: Frustrated magnets have garnered significant attention because of their potential to host exotic spin liquids, while many real material candidates exhibit magnetic orders. Due to their proximity to spin liquid phases, the semiclassical descriptions of these magnetic orders often fall short in capturing their intricate quantum behaviors. In this talk, I will introduce an improved mean-field method, named density-matrix mean-field theory (DMMFT), for these quantum magnets. Using local reduced density matrix, DMMFT can systematically incorporate the quantum fluctuations beyond conventional mean-field theories. Notably, it not only quantitatively evaluates the renormalization of order parameters induced by quantum fluctuations but also has the capability to detect the topological order of quantum phases. DMMFT offers an efficient approach to explore phases displaying unconventional quantum orders, particularly beneficial for investigating frustrated spin systems in high spatial dimensions.
Ref: https://arxiv.org/abs/2401.06236

Love and Naturalness
2024-05-17 10:30 - 12:00
Quantum Matter in Mathematics and Physics Seminar
Speaker: Mikhail Ivanov (MIT)
Title: Love and Naturalness
Abstract: Recent progress in gravitational wave astronomy has spurred the development of efficient tools to describe gravitational binary dynamics. One such tool is classical worldline effective field theory (EFT). In the first part of my talk, I will show how to use this EFT for systematic studies of tidal heating and deformations (Love numbers) of compact objects. I will present a gauge-invariant definition of Love numbers and show how to extract them in a coordinate-independent way from scattering amplitudes of the gravitational Raman process. I will show that the worldline EFT exhibits strong fine-tuning when applied to black holes. This gives rise to a naturalness paradox associated with the vanishing of black hole static Love numbers. In the second part of my talk, I will present a new symmetry of black holes (Love symmetry) that elegantly resolves this paradox. The Love symmetry is tightly connected to isometries of extremal black holes that appear in many holographic constructions. It also provides a curious example of IR/UV mixing, which may give insights for other hierarchy problems.

Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
2024-06-07 14:30 - 16:00
Quantum Matter in Mathematics and Physics Seminar
Speaker: Arkya Chatterjee (MIT)
Title: Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
Abstract: Non-invertible symmetries are often emergent at low-energies in gapless states of quantum matter. It is useful to construct lattice models that have these as exact symmetries in order to provide a UV-complete setting in which they are well-controlled. To that end, we propose to study one-dimensional Hamiltonians defined on tensor product Hilbert spaces with finite on-site dimension — referred to as “spin chains” in short — with exact non-invertible symmetries. We focus on two concrete examples: a spin chain with (invertible) S_3 symmetry and one with (non-invertible) Rep(S_3) symmetry. These models are largely analytically tractable and demonstrate all spontaneous symmetry breaking (SSB) phases of these symmetries. With the aid of tensor network algorithms, we systematically study the phase transitions between these SSB phases. Both models possess (intrinsically) non-invertible self-duality symmetries, for which we provide sequential circuit implementations. On the self-dual manifold in parameter space, we discover an incommensurate gapless phase with an anomalous U(1) symmetry which emanates from lattice translation.

Landscape of Tensor Network States Preparable from Measurement
2024-06-21 14:00 - 15:30
Quantum Matter in Mathematics and Physics Seminar
Speaker: Rahul Sahay (Harvard)

Title: Landscape of Tensor Network States Preparable from Measurement

Abstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk, we go beyond this, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. In 1D, a complete framework is developed for the case where a single round of measurements is the only entangling operation. Specifically, we completely classify the space of 1D preparable quantum states (forming a strict subset of all matrix product states), and characterize their physical constraints. In doing so, we find an intriguing physical trade-off between the richness of the preparable entanglement spectrum and correlation functions, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover, our classification enables one to search for and engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. We conclude by charting out generalizations, such as higher dimensional examples, considering multiple rounds of measurements, and implementing matrix product operators. At a high level, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].

Instanton in Lattice QCD from Higher Categories and Higher Anafunctors
2024-08-28 14:00 - 15:30
Speaker: Jing-Yuan Chen, Tsinghua University
Title: Instanton in Lattice QCD from Higher Categories and Higher Anafunctors

Abstract: Putting continuum QFT (not just TQFT) on the lattice is important for both fundamental understandings and practical numerics. The traditional way of doing so, based on simple intuitions, however, does not admit natural definitions for general topological operators of continuous-valued fields—one such example is the long standing problem in lattice QCD of lacking a natural definition for Yang-Mills instantons.
In this talk, I will explain a more systematic way to relate continuum and lattice QFT, based on higher categories and higher anafunctors, so that the topological operators in the continuum can be naturally defined on the lattice. The idea, though formulated formally, is physically very intuitive—we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum, so the higher categories that are employed to study higher homotopy theory should be naturally involved. Via this formalism, we resolve the long-standing problem of defining instanton (as well as Chern-Simons term) in lattice Yang-Mills theory, in terms of multiplicative bundle gerbes. Moreover, when the fields become discrete, our formalism can recover the Dijkgraaf-Witten and Turaev-Viro theory, so we hope this formalism to be a good starting point towards (in the very long term) a comprehensive categorical understanding of QFT that encompass both continuous and discrete degrees of freedom, applicable both to IR and to UV.

Classification and Construction of crystalline topological superconductors and insulators in interacting fermion systems
2024-09-20 14:00 - 15:30
Quantum Matter Seminar
Speaker: Zhengcheng Gu, Chinese University of Hong Kong
Title: Classification and construction of crystalline topological superconductors and insulators in interacting fermion systems
Abstract: The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this talk, I will discuss how to construct and classify crystalline topological superconductors (TSC) and topological insulators (TI) in interacting fermion systems. I will also discuss the relationship between internal symmetry protected SPT phases and crystalline symmetry protected SPT Phases.

Dolbeault Virasoro algebra and M5 branes
2024-10-11 09:00 - 10:00
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Brian Williams, Boston University
Title: Dolbeault Virasoro algebra and M5 branes
Abstract: The worldvolume theory on a stack of M5 branes in M-theory is superconformal. We propose a conjecture that in the holomorphic twist of the theory on a stack of M5 branes an infinite-dimensional enhancement of the (twisted) superconformal algebra is a symmetry. This algebra is closely related to the exceptional infinite-dimensional Lie superalgebra called E(3|6). We show that under the usual AGT correspondence this enhanced algebra degenerates to the Virasoro algebra at a particular central charge.
