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Entanglement guided search for parent Hamiltonians

Jul 16, 2018

6 pages

Published in:

Phys.Rev.Lett. 122 (2019) 15, 150606

Published: Apr 20, 2019

e-Print:

1807.06113 [quant-ph]

DOI:

10.1103/PhysRevLett.122.150606

View in:

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Abstract: (APS)

We introduce a method for the search of parent Hamiltonians of input wave functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between the reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several nontrivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave functions considerably simplifies the search for parent Hamiltonians.

Note:

5 pages, 5 figures, supplementary material

General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

References(65)

Figures(11)

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