Fractional Quantum Hall States with Two-Dimensional Isometric Tensor Networks
ORAL
Abstract
Studying topological phases beyond the Landau spontaneous symmetry breaking paradigm is a cornerstone of quantum many-body physics. As analytic non-perturbative field theory calculations are limited, so much of our understanding of exotic topologically ordered states relies on variational mean-field ansatz and numeric, with tensor networks emerging as powerful tools for this purpose. Fractional quantum hall (FQH) states embody a major class of topological phases that have been heavily studied via numerical methods, including one-dimensional matrix product states on cylinders [1], and it has only been recently that chiral spin liquids and bosonic FQH states were explored with two-dimensional projected entangled pair states [2,3]. In this work, we extend this ability by implementing interacting bosons coupled to gauge fields, probing bosonic Laughlin states among others, with 2D isometric tensor networks (isoTNS) [4,5]. Building on earlier characterization works for fractional Chern insulators in [6], we characterize ground state correlators along with dynamical spectral functions in these phases with our platform. As isoTNS directly maps to sequential quantum circuits [7], our work offers a practical route to efficiently simulate FQH correlators on quantum processors while providing a 2D classical platform for studying the rich physics of these strongly correlated topological phases.
[1] M. P. Zaletel and R. S. Mong. Phys. Rev. B 86, 245305 (2012).
[2] E. L. Weerda and M. Rizzi. Phys. Rev. B 109, L241117 (2024).
[3] J. Hasik, M. V. Damme, D. Poilblanc, and L. Vanderstraeten. Phys. Rev. Lett. 129, 177201 (2022).
[4] M. P. Zaletel and F. Pollmann. Phys. Rev. Lett. 124, 037201 (2020).
[5] SH. Lin, M. P. Zaletel, and F. Pollmann. Phys. Rev. B 106, 245102 (2022).
[6] X.-Y. Dong, A. G. Grushin, J. Motruk, and F. Pollmann. Phys. Rev. Lett. 121, 086401 (2018).
[7] S. Anand, J. Hauschild, Y. Zhang, A. C. Potter, M. P. Zaletel. Phys. Rev. X Quantum 4, 030334 (2023).
[1] M. P. Zaletel and R. S. Mong. Phys. Rev. B 86, 245305 (2012).
[2] E. L. Weerda and M. Rizzi. Phys. Rev. B 109, L241117 (2024).
[3] J. Hasik, M. V. Damme, D. Poilblanc, and L. Vanderstraeten. Phys. Rev. Lett. 129, 177201 (2022).
[4] M. P. Zaletel and F. Pollmann. Phys. Rev. Lett. 124, 037201 (2020).
[5] SH. Lin, M. P. Zaletel, and F. Pollmann. Phys. Rev. B 106, 245102 (2022).
[6] X.-Y. Dong, A. G. Grushin, J. Motruk, and F. Pollmann. Phys. Rev. Lett. 121, 086401 (2018).
[7] S. Anand, J. Hauschild, Y. Zhang, A. C. Potter, M. P. Zaletel. Phys. Rev. X Quantum 4, 030334 (2023).
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Presenters
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Zhifan F Yin
- University of California, Berkeley