Many-body localization from Hilbert- and real-space points of view

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• Ivan Khaymovich, Nordita
• Thursday 01 June 2023, 13:15-14:30
• on Zoom (please email Hannah for the Zoom link).

If you have a question about this talk, please contact Dr Hannah Price.

Many-body localization (MBL) is known to be a generic mechanism to break quantum thermalization and ergodicity. The seminal fruitful ideas, describing MBL as the Anderson localization in the Hilbert space have been recently revisited [1-2]. With help of Anderson orthogonality catastrophe, it has been shown that the Hilbert-space structure of the MBL eigenstate is characterized by a measure-zero, but extensive number of significantly occupied configurations. In other words, the wave-function Hilbert-space support set is given by a certain fractal with the corresponding Hausdorff dimension and this is the way how the MBL breaks down the Hilbert-space ergodicity. On the other hand, the well-established and accepted by the community picture of emergent set of local integrals of motion [3] provides the structure of the MBL in the real space.

In this talk, I will provide the observable (later measured in the experiment [4]) which combines the fractality in the Hilbert space with the presence of local integrals of motion [2]. This observable being the radial profile of the eigenstate over the Hamming distance keeps the information about both the Hilbert-space fractal dimensions and the real-space localization length and uncovers the structure of these measures across the MBL transition. Phenomenological picture behind this behavior is consistent with the Kosterlitz-Thouless scenario of the MBL transition, suggested in the literature.

Literature: [1] N. Macé, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 123, 180601 (2019). [2] G. De Tomasi, I. M. Khaymovich, F. Pollmann, S. Warzel, Phys. Rev. B 104 , 024202 (2021). [3] D. Abanin, E. Altman, I. Bloch, M. Serbyn, Rev. Mod. Phys. 91, 021001 (2019). [4] Y. Yao et al arXiv:2211.05803 (2022).

This talk is part of the Theoretical Physics Seminars series.

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• Bham Talks
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• on Zoom (please email Hannah for the Zoom link)

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