We present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wave function with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling and obtain more accurate effective spin models than the standard perturbative approach.

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• Electronic structure
• Quantum circuits
• Strongly correlated systems
• Density matrix renormalization group
• Electron-correlation calculations
• Hubbard model
• Tensor network methods
• t-J model