Landscape of Tensor Network States Preparable from Measurement
2024-06-21 14:00 - 15:30 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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.
