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DTSTART;TZID=America/New_York:20240607T143000
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CREATED:20240529T212219Z
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UID:10003392-1717770600-1717776000@cmsa.fas.harvard.edu
SUMMARY:Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Arkya Chatterjee (MIT) \nTitle: Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries \nAbstract: 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. \n 
URL:https://cmsa.fas.harvard.edu/event/qmmp_6724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-06.07.2024.png
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DTSTART;TZID=America/New_York:20240621T140000
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CREATED:20240620T133636Z
LAST-MODIFIED:20240620T133710Z
UID:10003393-1718978400-1718983800@cmsa.fas.harvard.edu
SUMMARY:Landscape of Tensor Network States Preparable from Measurement
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Rahul Sahay (Harvard)\n\nTitle: Landscape of Tensor Network States Preparable from Measurement\n\nAbstract: 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].\n 
URL:https://cmsa.fas.harvard.edu/event/qm_62124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-06.21.2024.png
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