Restoring permutational invariance in the Jordan–Wigner transformation

Henderson, Thomas M.; Gao, Fei; Scuseria, Gustavo E.

doi:10.1080/00268976.2023.2254857

Restoring permutational invariance in the Jordan–Wigner transformation

Journal Article · Tue Sep 05 00:00:00 EDT 2023 · Molecular Physics

DOI:https://doi.org/10.1080/00268976.2023.2254857· OSTI ID:2349221

^[1]; Gao, Fei ^[2]; ^[2]

Rice University, Houston, TX (United States); Rice University
Rice University, Houston, TX (United States)

The Jordan–Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the labelling of the spins. One consequence of this dependence is that approximate solutions of a Jordan–Wigner-transformed Hamiltonian may depend on the (physically inconsequential) labelling of the spins. In this work, we turn to an extended Jordan–Wigner transformation which remedies this problem and which may also introduce some correlation atop the Hartree–Fock solution of a transformed spin Hamiltonian. We demonstrate that this extended Jordan–Wigner transformation can be thought of as arising from a unitary version of the Lie algebraic similarity transformation (LAST) theory. Here, we show how these ideas, particularly in combination with the standard (non-unitary) version of LAST, can provide a potentially powerful tool for the treatment of the XXZ and J₁–J₂ Heisenberg Hamiltonians.

View Accepted Manuscript (DOE)

Research Organization:: Emory University, Atlanta, GA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019374; SC0001474; SC0001474

OSTI ID:: 2349221

Journal Information:: Molecular Physics, Journal Name: Molecular Physics Journal Issue: 7-8 Vol. 122; ISSN 0026-8976

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

References (30)

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry Paldus, Josef; Li, Xiangzhu; Prigogine, I. Advances in Chemical Physics: Prigogine/Advances https://doi.org/10.1002/9780470141694.ch1	book	January 1999
�ber das Paulische �quivalenzverbot Jordan, P.; Wigner, E. Zeitschrift f�r Physik, Vol. 47, Issue 9-10 https://doi.org/10.1007/BF01331938	journal	September 1928
Nonunitary bogoliubov transformations and extension of Wick’s theorem Balian, R.; Brezin, E. Il Nuovo Cimento B Series 10, Vol. 64, Issue 1 https://doi.org/10.1007/BF02710281	journal	November 1969
The coupled cluster method applied to quantum magnetism Farnell, Damian J. J.; Bishop, Raymond F. Quantum Magnetism https://doi.org/10.1007/BFb0119597	book	January 2004
Accelerating the convergence of the coupled-cluster approach Scuseria, Gustavo E.; Lee, Timothy J.; Schaefer, Henry F. Chemical Physics Letters, Vol. 130, Issue 3 https://doi.org/10.1016/0009-2614(86)80461-4	journal	October 1986
Stability conditions and nuclear rotations in the Hartree-Fock theory Thouless, D. J. Nuclear Physics, Vol. 21 https://doi.org/10.1016/0029-5582(60)90048-1	journal	November 1960
On the use of general symmetry-projected Hartree–Fock–Bogoliubov configurations in variational approaches to the nuclear many-body problem Schmid, K. W. Progress in Particle and Nuclear Physics, Vol. 52, Issue 2 https://doi.org/10.1016/j.ppnp.2004.02.001	journal	April 2004
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Quantum Chemistry in the Age of Quantum Computing Cao, Yudong; Romero, Jonathan; Olson, Jonathan P. Chemical Reviews, Vol. 119, Issue 19 https://doi.org/10.1021/acs.chemrev.8b00803	journal	August 2019
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science Bauer, Bela; Bravyi, Sergey; Motta, Mario Chemical Reviews, Vol. 120, Issue 22 https://doi.org/10.1021/acs.chemrev.9b00829	journal	October 2020
Generalized Hartree–Fock Description of Molecular Dissociation Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E. Journal of Chemical Theory and Computation, Vol. 7, Issue 9 https://doi.org/10.1021/ct200345a	journal	July 2011
On Next‐Nearest‐Neighbor Interaction in Linear Chain. I Majumdar, Chanchal K.; Ghosh, Dipan K. Journal of Mathematical Physics, Vol. 10, Issue 8 https://doi.org/10.1063/1.1664978	journal	August 1969
Transposition of the Theories Describing Superconducting Systems to Molecular Systems. Method of Biorbitals Bratož, S.; Durand, Ph. The Journal of Chemical Physics, Vol. 43, Issue 8 https://doi.org/10.1063/1.1697193	journal	October 1965
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers Coleman, A. J. Journal of Mathematical Physics, Vol. 6, Issue 9 https://doi.org/10.1063/1.1704794	journal	September 1965
Projected quasiparticle theory for molecular electronic structure Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M. The Journal of Chemical Physics, Vol. 135, Issue 12 https://doi.org/10.1063/1.3643338	journal	September 2011
Projected Hartree–Fock theory Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Tsuchimochi, Takashi The Journal of Chemical Physics, Vol. 136, Issue 16 https://doi.org/10.1063/1.4705280	journal	April 2012
Relation between fermionic and qubit mean fields in the electronic structure problem Ryabinkin, Ilya G.; Genin, Scott N.; Izmaylov, Artur F. The Journal of Chemical Physics, Vol. 149, Issue 21 https://doi.org/10.1063/1.5055357	journal	December 2018
Exploring non-linear correlators on AGP Khamoshi, Armin; Chen, Guo P.; Henderson, Thomas M. The Journal of Chemical Physics, Vol. 154, Issue 7 https://doi.org/10.1063/5.0039618	journal	February 2021
Strong–weak duality via Jordan–Wigner transformation: Using fermionic methods for strongly correlated su(2) spin systems Henderson, Thomas M.; Chen, Guo P.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 157, Issue 19 https://doi.org/10.1063/5.0125124	journal	November 2022
Robust formulation of Wick’s theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctions Chen, Guo P.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 158, Issue 23 https://doi.org/10.1063/5.0156124	journal	June 2023
Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects Löwdin, Per-Olov Physical Review, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRev.97.1509	journal	March 1955
Fermionic interpretation of the quantum phase transition in XXZ magnets Yang, Tao; Wang, Bangming; Song, Peng Physical Review B, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevB.106.144438	journal	October 2022
Exploring spin antisymmetrized geminal power Ansätze for strongly correlated spin systems Liu, Zhiyuan; Gao, Fei; Chen, Guo P. Physical Review B, Vol. 108, Issue 8 https://doi.org/10.1103/PhysRevB.108.085136	journal	August 2023
Ground state of the two-dimensional antiferromagnetic Heisenberg model studied using an extended Wigner-Jordon transformation Wang, Y. R. Physical Review B, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevB.43.3786	journal	February 1991
Phase transitions in the spin-halfJ1−J2model Bishop, Raymond F.; Farnell, Damian J. J.; Parkinson, John B. Physical Review B, Vol. 58, Issue 10 https://doi.org/10.1103/PhysRevB.58.6394	journal	September 1998
Ground state phases of the spin-1/2 J 1 – J 2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment Darradi, R.; Derzhko, O.; Zinke, R. Physical Review B, Vol. 78, Issue 21 https://doi.org/10.1103/PhysRevB.78.214415	journal	December 2008
Lie algebraic similarity transformed Hamiltonians for lattice model systems Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M. Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.041114	journal	January 2015
Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- 1 2 J 1 − J 2 Square Heisenberg Model Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.027201	journal	July 2014
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/RevModPhys.79.291	journal	February 2007
The spin-1/2 square-lattice J1-J2 model: the spin-gap issue Richter, Johannes; Zinke, Ronald; Farnell, Damian J. J. The European Physical Journal B, Vol. 88, Issue 1 https://doi.org/10.1140/epjb/e2014-50589-x	journal	January 2015

Similar Records

Fermionic mean-field theory as a tool for studying spin Hamiltonians

Journal Article · Tue Dec 17 23:00:00 EST 2024 · Journal of Chemical Physics · OSTI ID:2482096

Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

Journal Article · Tue Nov 01 00:00:00 EDT 2022 · Journal of Chemical Physics · OSTI ID:1895606

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
Jordan–Wigner transformation
lattice models
spin systems

Restoring permutational invariance in the Jordan–Wigner transformation

Citation Formats

References (30)

Similar Records

Related Subjects