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
Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions. / Chertkov, Eli; Clark, Bryan K.
In: Physical Review X, Vol. 8, No. 3, 031029, 27.07.2018.Research output: Contribution to journal › Article
}
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.
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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 -