Speaker
Description
The dynamics of quantum many-body systems are strongly constrained by the conserved quantities and symmetries of their Hamiltonians. Conserved quantities play a fundamental role in phenomena such as thermalization/nonthermalization, transport, and integrability, while the commutation relations among conserved quantities are closely related to continuous symmetries and the underlying algebraic structure of the system. In practice, however, information obtained from experiments and numerical simulations is generally limited to the time evolution of expectation values of a subset of observables, making it difficult to infer conserved quantities and the associated symmetry structure directly from the data.
Recent advances in machine learning have led to the development of powerful methods for analyzing physical systems. In quantum many-body physics, in particular, considerable progress has been made in Hamiltonian reconstruction from observational data [1]. By contrast, methods for inferring conserved quantities and symmetry structures from data have been developed mainly for classical dynamical systems [2-4]. Existing studies on quantum systems are limited to identifying conserved quantities with local support [5] and a general framework for inferring multiple conserved quantities together with their algebraic structure remains unavailable.
In this presentation, we propose a method for inferring multiple independent conserved quantities and the Lie algebra they generate from time-series data of expectation values in quantum many-body systems. Our approach combines Hamiltonian reconstruction with techniques for inferring conserved quantities and Lie algebraic structures originally developed for classical dynamical systems. Specifically, the proposed method consists of three steps: (i) reconstructing the Hamiltonian from time-series data of expectation values; (ii) parameterizing and optimizing conserved quantities so that they commute with the reconstructed Hamiltonian while remaining mutually independent; and (iii) computing the structure constants of the inferred conserved quantities to identify the underlying Lie algebra. Finally, we evaluate the proposed method using numerically generated time-series data of expectation values for both spin and fermionic systems.
[1] Rishabh Gupta et al., The Journal of Physical Chemistry A, 127 (2023)
[2] Artem Moskalev et al., arXiv:2210.04345
[3] Manu Bhat et al., arXiv:2504.10777
[4] Wanda Hou et al., arXiv:2412.14632
[5] T. E. O’Brien et al., Physical Review B, 94 (2016)