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Infinite Analysis Lab (Ogata)
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The lab studies topological phases of quantum spin systems with mathematical rigor.
AboutAbout the lab
Classifying the phases of quantum spin systems with mathematics.
The Ogata Lab studies quantum spin systems, a fundamental model of quantum statistical mechanics, in the field of mathematical physics.
It focuses on the state of matter cooled to absolute zero (the ground state) and the gap just above its energy (the spectral gap).
Models with a spectral gap are also related to quantum computers that are robust against noise, and the lab works on the problem of classifying such models.
The lab pursues research that shows, with mathematical rigor, what physicists have conjectured.
Key terms
- Quantum spin system
- A basic mathematical model of quantum statistical mechanics that describes, using quantum mechanics, a material in which small magnets (spins) are arranged.
- Spectral gap
- The gap between the lowest energy and the rest of the energies. A model that has one can be regarded as stable in a certain sense.
- Topological phase
- When models that can be connected without closing the gap are regarded as the same, a class that does not include the trivial model.
- Anyon
- A quasiparticle that appears in two-dimensional systems. It provides a clue (an invariant) for classifying topological phases.
NewsLab news
Professor Ogata received the ICBS Frontier of Science Award
Professor Ogata received the Asahi Prize
Professor Ogata received the Saruhashi Prize
Professor Ogata received the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (Prize for Science and Technology)
ResearchResearch themes
The lab studies quantum spin systems, fundamental models of quantum statistical mechanics, and works on the classification problem for models whose ground state has a spectral gap. For symmetry-protected phases and topological phases, it proves with mathematical rigor what physicists have conjectured.
*Illustrative imageClassification of Gapped Models
The lab studies a classification problem in which two models connected by a smooth path without closing the spectral gap are regarded as equivalent.
*Illustrative imageInvariants of Symmetry-Protected Phases
The lab has proved with mathematical rigor the physicists' conjecture that symmetry-protected phases of quantum spin systems in one and two spatial dimensions have invariants taking values in cohomology.
*Illustrative imageDerivation of Anyons
For models satisfying a condition called approximate Haag duality, the lab derived the quasiparticles called anyons in a general setting.
*Illustrative imageBulk-Boundary Correspondence of Anyons
For two-dimensional topological phases, the lab proved the bulk-boundary correspondence of anyons known as the Kitaev–Kong conjecture, within its own framework.
MembersFaculty
- ProfessorYoshiko Ogata
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Thousands of Atoms Swap 'Spins' with Partners in Quantum Square Dance ( )” National Institute of Standards and Technology / Public domain (cropped)
- Classification of Gapped Models: “Spin chain3” Tluck074 / CC BY-SA 4.0 (cropped)
- Invariants of Symmetry-Protected Phases: “ToricCodeLattice” Woottonjames / CC BY 3.0 (cropped)
- Derivation of Anyons: “String diagrams for braiding” Meelo Mooses / CC BY-SA 4.0 (cropped)
- Bulk-Boundary Correspondence of Anyons: “ToricCodeTorus” Woottonjames / CC BY 3.0 (cropped)
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