Jun 10 – 15, 2018
Tsinghua Sanya International Mathematics Forum
Asia/Shanghai timezone

Reverse engineering Hamiltonian from spectrum

Jun 14, 2018, 11:15 AM
45m
Tsinghua Sanya International Mathematics Forum

Tsinghua Sanya International Mathematics Forum

Sanya, Hainan, China

Speaker

Hiroyu Fujita (University of Tokyo)

Description

Handling the large number of degrees of freedom with proper approximations, namely the construction of the effective Hamiltonian is at the heart of the (condensed matter) physics. Here we propose a simple scheme of constructing Hamiltonians from given energy spectrum. The sparse nature of the physical Hamiltonians allows us to formulate this as a solvable supervised learning problem. Taking a simple model of correlated electron systems, we demonstrate the data-driven construction of its low-energy effective model. Moreover, we find that the same approach works for the construction of the entanglement Hamiltonian of a given quantum many-body state from its entanglement spectrum. Compared to the known approach based on the full diagonalization of the reduced density matrix, our one is computationally much cheeper thus offering a way of studying the entanglement nature of large (sub)systems under various boundary conditions.

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