Journal
PHYSICAL REVIEW RESEARCH
Volume 2, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevResearch.2.043258
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Funding
- National Science Foundation [DMR-2038011, OAC-1934714]
- ARO [W911NF-20-1-0163]
- Harvard-MIT Center for Ultracold Atoms
- Postdoctoral Fellowship in Quantum Science of the Harvard-MPQ Center for Quantum Optics
- Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering
- EU through the ERC Advanced Grant QUENOCOBA [742102]
- U.S. Department of Energy Office of Science User Facility [DE-AC02-05CH11231]
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We propose a numerical method which embeds the variational non-Gaussian wave-function approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wave function that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wave function exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.
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