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Quantum Spin Chains and von Neumann Algebra Lieb-Schultz-Mattis type theorem without continuous symmetry Hal Tasaki Quantum Information and String Theory 2019 (YITP , June 10) Yoshiko Ogata and Hal Tasaki, LiebSchultzMattis Type

  1. Quantum Spin Chains and 
 von Neumann Algebra Lieb-Schultz-Mattis type theorem without continuous symmetry Hal Tasaki Quantum Information and String Theory 2019 (YITP , June 10) Yoshiko Ogata and Hal Tasaki, “Lieb–Schultz–Mattis Type Theorems for Quantum Spin Chains Without Continuous Symmetry” 
 arXiv:1808.08740, Commnun. Math. Phys.

  2. Lieb-Schultz-Mattis Theorem and its Generalizations

  3. eTW1jc2t/LbhZ3dvf2D4uFRU8epYthgsYhVO6AaBZfYMNwIbCcKaRQIbAWj25nfekKleSwfzDhBP6IDyUPOqLFS/a5XL l dw6ySryMlCBDrVf86vZjlkYoDRNU647nJsafUGU4EzgtdFONCWUjOsCOpZJGqP3J/NApObNKn4SxsiUNmau/JyY0 nocBbYzomaol72Z+J/XSU147U+4TFKDki0WhakgJiazr0mfK2RGjC2hTHF7K2FDqigzNpuCDcFbfnmVNCtl76JcqV+WqjdZH k4gVM4Bw+uoAr3UIMGMEB4hld4cx6dF+fd+Vi05pxs5hj+wPn8AZo7jM0=</latexit> <latexit sha1_base64="4COX8krFob56QE/RjaUfoakOjHE=">A B6HicbVDLSgNBEOyNrxhfUY9eBoPgKexGQY9BETwmYB6QLGF20puMmZ1dZmaFEPIFXjwo4tVP8ubfOEn2oIkFDUV N91dQSK4Nq7 <latexit sha1_base64="oW7OyFl8fZOuY5qYrNXg+guGckE=">A CUXicbVFNSyNBFKzMrqtG3Y27Ry+NYWFBCDMqrAcPosh6VHajQgyhp/NG 3u6h+4eIQz5Of4dD3ryf3jxoNiJOajZBw+q +r1R3VaKOl8HN/Xok+fZ7 Mzs3XFxaXvn5rLH8/dqa0gtrCKGNPU+5ISU1tL72i08ISz1NFJ+nl3kg/uSLrpNH/ KCgbs7Ptcyk4D5QprGJf RQ4RoWORj+4C+G2A5oP/Q1FGiMpz1rYZ0FhkO80Q MNBw8WsEz4insoTDsNZpxKx4XmwbJBDQxqcNe4/asb0SZk/ZCcec6SVz4bsWtl0LRsH5WOiq4uOTn1AlQ85xctxonMmQ/A9NnmbGhtWdj9u1ExXPnBnkanDn3F+6jNiL/p3VKn21 K6mL0pMWrwdlpWLesFG8rC8tCa8GAXBhZbgrExfc uHDJ9RDCMnHJ0+D4/VWstFaP9ps7uxO4pjDClbxCwl+YwcHOEQ7RH2DBz huXZXe4wQRa/WqDaZ+YF3FS28ALoIoeA=</latexit> <latexit sha1_base64="NXTrv9Kj2M3yUuGx7lK6sUlpWhk=">A B83icbVA9SwNBEJ3zM8avqKXNYhCswl0stBAM2lhYRDAfkISwt5lLluztHbt7Qj yN2wsFNHSP2PnT7Fzc0mhiW8YeLw3w84+PxZcG9f9cpaWV1bX1nMb+c2t7Z3dwt5+XUeJYlhjkYhU06caBZdYM9wIbMYKaegLbPjD64nfeECleSTvzSjGTkj7kgecUWOlAN4BQdi6gNtuoeiW3Axk XgzUrz8DjJUu4XPdi9iSYjSMEG1bnlubDopVY zgeN8O9EYUzakfWxZKm IupNmN4/JsV 6JIiUbWlIpv7eSGmo9Sj07WRIzUDPexPxP6+VmOC8k3IZJwYlmz4UJIKYiEwCID2ukBkxsoQyxe2thA2o szYmPI2BG/+y4ukXi5 p6XynVusXMEUOTiEIzgBD86gAjdQhRowiOERnuHFSZwn59V5m4 uObOdA/gD5+MHah6TAg= </latexit> <latexit sha1_base64="v5k/ZYLo3oNoxufJdYJcSZ4BQCU=">A CQXicdZE7SwNBEMfn4ivGV9RCxOYwCBYh3CWIaYSgjWVE84AkhL3NXrJk7/bY3RPCkY/j17DxC4idNjYW ihia+PmUZhEB3b485sZ ve/TsCoVJb1aMTm5hcWl+L iZXVtfWN5OZW fJQYFLCnHFRdZAkjPqkpKhipBoIgjyHkYrTPRvUK9dESMr9K9ULSMNDbZ+6FCOlEU+m4RJO4AZcEIA QwQ29HXO6pye4Ll/+NE Z9ACDgpkM5myMtYwzFlhj0WqkH+ 3 l63S02kw/1FsehR3yFGZKyZluBakRIKIoZ6SfqoSQBwl3UJjUtfeQR2YiGDvTNA01apsuFPr4yh/T3RIQ8KXueozs9pDpyujaAf9VqoXLzjYj6QaiIj0eL3JCZipsDO80WFQ r1tMCYUH1XU3cQ JhpU1PaBPs6SfPinI2Y+cy2QvtximMIg57sA+H+jO oQDnUIS NvsWXuAdPow74834NL5GrTFjPLMNE2F8/wBPaKW5</latexit> <latexit sha1_base64="wV+VUxihJVK86dDwFBvHtk0X8dg=">A Lieb-Schultz-Mattis (LSM) type theorem No-go theorem which states that certain quantum many- body systems CANNNOT have a gapped unique ground state NO HALDANE GAP!! ∆ E = O (1) the original theorem Lieb, Schultz, Mattis 1961, A ffm eck, Lieb 1986 antiferromagnetic Heisenberg chain S = 1 2 , 3 2 , 5 H = P L ˆ j =1 ˆ S j · ˆ with S j +1 2 , . . . for any , there exists an energy eigenvalue ` < L E such that E GS < E ≤ E GS + const . ` CB3icbVC7TsMwFL0pr1KgLTDCEFEhMV JGWCsysLAUCT6kNqoclynterYke2Aq gbCx/CwsIAQl35BTb+hIEB9zFAy7EsHZ9zr67v8SNGlXacTyu1srq2vpHezGxt72Rz+d29uhKx KSGBROy6SNFGOWkpqlmpBlJgkKfkY /uJj4jVsiFRX8Rg8j4oWox2lAMdJGEvkcXMEjxBABAm OgDvzpsAhA 3DTr7gFJ0p7GXizkmhfDiuON9f2Won/9HuChyHhGvMkFIt14m0lyCpKWZklGnHikQID1CPtAzlKCTKS6Z7jOxjo3TtQEhzuban6u+OBIVKDUPfVIZI9 WiNxH/81qxDs69hPIo1oTj2aAgZrYW9iQUu0slwZoNDUFYUvNXG/eR Fib6DImBHdx5WVSLxXd02Lp2qR gRnScABHcAIunE ZLqEKNcBwD0/wAq/Wg/VsvVnjW nKmvfswx9Y7z9OoZgw</latexit> there are gapless excitations in the limit L ↑ ∞

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