期刊
PHYSICAL REVIEW X
卷 8, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.8.031029
关键词
Computational Physics; Condensed Matter Physics; Quantum Physics
资金
- SciDAC [DE-FG02-12ER46875]
- National Science Foundation [OCI-0725070, ACI-1238993]
- state of Illinois
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 vertical bar Psi(T) and produces as output Hamiltonians for which vertical bar Psi(T) 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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