Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems
The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Here, our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.
- Research Organization:
- Rice Univ., Houston, TX (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- FG02-09ER16053; SC0001474
- OSTI ID:
- 1895606
- Alternate ID(s):
- OSTI ID: 1898917
- Journal Information:
- Journal of Chemical Physics, Vol. 157, Issue 19; ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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