### Abstract

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.

Original language | English (US) |
---|---|

Article number | 031029 |

Journal | Physical Review X |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Jul 27 2018 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review X*,

*8*(3), [031029]. https://doi.org/10.1103/PhysRevX.8.031029

**Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions.** / Chertkov, Eli; Clark, Bryan K.

Research output: Contribution to journal › Article

*Physical Review X*, vol. 8, no. 3, 031029. https://doi.org/10.1103/PhysRevX.8.031029

}

TY - JOUR

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

AU - Chertkov, Eli

AU - Clark, Bryan K.

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.

UR - http://www.scopus.com/inward/record.url?scp=85051060628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051060628&partnerID=8YFLogxK

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 -