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Physical review. B./Physical review. B

Reconstructing spin Hamiltonians of two-dimensional Gutzwiller-projected wave functions

Lucas Z. Brito, John Bradley Marston

Published May 26, 2026• 0 citations
Publisher
DOI
10.1103/qcjl-cklq

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Construction of Spin Eigenfunctions by the Projection Operator Method

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We apply the correlation matrix Hamiltonian reconstruction technique to the two-dimensional Gutzwiller-projected Fermi sea and π-flux states on finite-sized square and triangular lattices. Our results indicate no spin Hamiltonian with simple local interaction terms stabilizes such states for finite system sizes. We develop a quantitative assessment of the importance of local interactions to the stabilization of these liquid states. Lastly, we systematically assess arguments for the origin of local terms driving a Gutzwiller-projected ground state.
We introduce a method to design a local spin Hamiltonian to realize a Gutzwiller-projected parton wave functions (GPWF) as its ground state. For example, the Dirac spin liquid (DSL) state is quite close to the true ground state of the spin-1/2 Heisenberg model on kagome lattice. We examine what kind of perturbations we should add in order to drive the DSL to more stable chiral spin liquid (CSL), valence bond solid (VBS) or Gutzwiller-projected spin Hall (GSH) states. We compute the two-body reduced-density-matrices (2-RDM) of GPWFs for those target states, and compare them to the 2-RDM of the DSL. This allows us to design local spin models with only two-body interactions that may realize those interesting target states. Our results agree very well with recent numerical calculations for CSL on kagome lattice. We also study spin-1 systems on kagome lattice, and design local spin models that may realize CSL, VBS and symmetry-protected topological (SPT) states. Our work establishes a directional guide for further numerical simulations.
Recent experiments strongly suggest that a Fermi-surface reconstruction and multiple Fermi pockets are important common features of the underdoped high-temperature cuprate superconductors. A related theoretical work [Phys. Rev. B 79, 134512 (2009)] has demonstrated that a number of hallmark phenomena observed in the underdoped cuprates appear naturally in the scenario of a paired electron pocket coexisting with unpaired hole pockets. We propose Gutzwiller-projected wave functions to describe this two-fluid state as well as two competing states in its vicinity. It is argued that a pseudogap state constructed from these wave functions may be selected by energetics at finite temperatures due to spin fluctuations.