Automatic design of Hamiltonians

Kiryl Pakrouski

Department of Physics, Princeton University, Princeton, NJ 08544, USA

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We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties specifying thereby the search query. Using fractional quantum Hall effect as a test system we illustrate how the framework can be used to determine a generating Hamiltonian of a finite-size model wavefunction (Moore-Read Pfaffian and Read-Rezayi states), find optimal conditions for an experiment or "extrapolate" given wavefunctions in a certain universality class from smaller to larger system sizes. We also discuss how the search for approximate generating Hamiltonians may be used to find simpler and more realistic models implementing the given exotic phase of matter by experimentally accessible interaction terms.

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[1] Jonas B. Rigo and Andrew K. Mitchell, "Machine learning effective models for quantum systems", Physical Review B 101 24, 241105 (2020).

[2] Xhek Turkeshi and Marcello Dalmonte, "Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions", SciPost Physics 8 3, 042 (2020).

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