TY - JOUR

T1 - Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

AU - Chertkov, Eli

AU - Clark, Bryan K.

N1 - Publisher Copyright:
© 2018 authors. Published by the American Physical Society.

PY - 2018/7/27

Y1 - 2018/7/27

N2 - Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational "inverse method," the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function |ψT and produces as output Hamiltonians for which |ψT is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and, in this work, we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model. EHC gives an alternative inverse approach for studying quantum many-body phenomena.

AB - Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational "inverse method," the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function |ψT and produces as output Hamiltonians for which |ψT is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and, in this work, we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model. EHC gives an alternative inverse approach for studying quantum many-body phenomena.

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U2 - 10.1103/PhysRevX.8.031029

DO - 10.1103/PhysRevX.8.031029

M3 - Article

AN - SCOPUS:85051060628

VL - 8

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 3

M1 - 031029

ER -