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arXiv:2409.15424 · Physical review. B./Physical review. B

Quantum-interference-induced pairing in bosonic doped antiferromagnets

Hao-Kai Zhang, Jia-Xin Zhang, Ji-Si Xu, Hong‐Chen Jiang, Zheng-Yu Weng

Published Nov 21, 2025• 3 citations
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Abstract

The pairing mechanism in doped antiferromagnets is essential for understanding high-temperature superconductivity. In this work, we investigate the pairing mechanism in bosonic doped antiferromagnets via large-scale density matrix renormalization group calculations of the bosonic $t\ensuremath{-}J$ model. We discover a pair density wave (PDW) coexists with the antiferromagnetic (AFM) order forming a ``supersolid'' at small doping. The pairing is attributed to a hidden many-body Berry phase that introduces the sole ``sign problem'' into this bosonic model and imposes quantum phase frustration to the spin-charge interference pattern. Only via tightly pairing of doped holes can such frustration be most effectively erased in an AFM background. By contrast, the pairing vanishes as the Berry phase is trivialized in the ferromagnetic condensate at larger doping or switched off into the Bose-Hubbard model at large $U$. The present pairing mechanism---distinct from the conventional mechanisms based on Fermi surface instabilities---may provide a different perspective and new insights for understanding the complex nature of doped Mott insulators and is promising to be probed on qudit-based quantum simulators such as ultracold Rydberg atom arrays.

DOI
10.1103/1mc9-xqhy

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The pairing mechanism in doped antiferromagnets is essential for understanding high-temperature superconductivity. In this work, we investigate the pairing mechanism in bosonic doped antiferromagnets via large-scale density matrix renormalization group calculations of the bosonic t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. We discover a pair density wave (PDW) coexists with the antiferromagnetic (AFM) order forming a supersolid'' at small doping. The pairing is attributed to a hidden many-body Berry phase that introduces the sole sign problem'' into this bosonic model and imposes quantum phase frustration to the spin-charge interference pattern. Only via tightly pairing of doped holes can such frustration be most effectively erased in an AFM background. By contrast, the pairing vanishes as the Berry phase is trivialized in the ferromagnetic condensate at larger doping or switched off into the Bose-Hubbard model at large UUU. The present pairing mechanism---distinct from the conventional mechanisms based on Fermi surface instabilities---may provide a different perspective and new insights for understanding the complex nature of doped Mott insulators and is promising to be probed on qudit-based quantum simulators such as ultracold Rydberg atom arrays.
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Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.
We apply the fermionic tensor network (TN) state method to understand the strongly correlated nature in a doped Mott insulator. We conduct a comparative study of the $\ensuremath{\sigma}t\text{\ensuremath{-}}J$ model, in which the no-double-occupancy constraint remains unchanged but the quantum phase string effect associated with doped holes is precisely switched off. Thus, the ground state of the $\ensuremath{\sigma}t\text{\ensuremath{-}}J$ model can serve as a well-controlled reference state of the standard $t\text{\ensuremath{-}}J$ model. In the absence of the phase string, the spin long-range antiferromagnetic (AFM) order is found to be essentially decoupled from the doped holes, and the latter contribute to a Fermi-liquid-like compressibility and a coherent single-particle propagation with a markedly reduced pairing tendency. In contrast, our TN calculations of the $t\text{\ensuremath{-}}J$ model indicate that the AFM order decreases much faster with doping and the single-particle propagation of doped holes gets substantially suppressed, concurrently with a much stronger charge compressibility at small doping and significantly amplified Cooper pairing tendencies. These findings demonstrate that quantum many-body interference from phase strings plays a pivotal role in the $t\text{\ensuremath{-}}J$ model, mediating long-range entanglement between spin and charge degrees of freedom, which might hold the key mechanism for high-Tc{T}_{c}Tc​ cuprates.
Unraveling the microscopic mechanisms governing the physics of doped quantum magnets is key to advancing our understanding of strongly correlated quantum matter. Quantum simulation platforms, e.g., ultracold atoms in optical lattices or tweezer arrays, provide a powerful tool to investigate the interplay between spin and charge motion in microscopic detail. Here, in a twist, we disentangle the role of particle statistics from the physics of strong correlations by exploring the strong coupling limit of doped bosonic quantum magnets, specifically the antiferromagnetic (AFM) bosonic t − J model. Using large-scale density matrix renormalization group calculations, we map out the phase diagram on the two-dimensional square lattice at finite doping. In the low-doping regime, bosonic holes form partially filled stripes, akin to those observed in high- T c cuprates. As doping increases, a transition occurs to a partially polarized ferromagnetic (FM) phase, driven by the motion of mobile bosonic charge carriers forming Nagaoka polarons. At high doping or large t / J , the system evolves into a fully polarized FM. These findings shed light on the role of particle statistics in strongly correlated many-body systems, revealing connections to stripe formation and the physics of kinetic (Nagaoka-type) ferromagnetism. Our results may be realized in state-of-the-art quantum simulation platforms, including bosonic quantum gas microscopes, Rydberg atom tweezer arrays, and ultracold polar molecules, paving the way for future experimental studies of doped bosonic quantum magnets.
Pair-density-wave (PDW) superconductivity is a state in which the superconducting order parameter modulates at a finite wavevector. Using large-scale density matrix renormalization group, we study the doped altermagnetic Mott insulator in the checkerboard ttt-JJJ model, where altermagnetic exchange anisotropy is encoded microscopically through anisotropic ferromagnetic next-nearest-neighbor exchange. By mapping the ground-state phase diagram as a function of doping and altermagnetic anisotropy, mainly on six-leg cylinders, we identify a transition from a uniform ddd-wave superconducting regime with charge modulation to a PDW regime coexisting with stripe order. In the PDW regime, we report an unconventional wave-vector locking QPDW≈2QStripe\mathbf Q_{\mathrm{PDW}}\approx 2\mathbf Q_{\mathrm{Stripe}}QPDW​≈2QStripe​ along the cylinder direction, in contrast to the conventional relation. Pair correlations reveal a two-scale structure, consisting of short-distance local ddd-wave pairing and long-distance finite-momentum PDW correlations. A symmetry-based Ginzburg--Landau analysis is presented for the observed locking. Our results identify altermagnetism as a strong-coupling, microscopically grounded route to finite-momentum superconductivity in doped Mott insulators.
Antiferromagnetism and superconductivity are often viewed as competing orders in correlated electron systems. Here, we demonstrate that kinetic frustration in hole motion facilitates their coexistence within the square-lattice repulsive Hubbard model. Combining exact analytical solutions on tailored geometries with large-scale numerical simulations, we reveal a robust pairing mechanism: Holes on opposite sublattices behave as if they carry opposite effective charges due to spin singlet formation from kinetic frustration. This emergent property suppresses phase separation and fosters a coherent [Formula: see text]-wave superconducting channel embedded within a long-range antiferromagnetic background. Our findings establish a minimal yet broadly applicable framework for stabilizing strong-coupling superconductivity in doped Mott insulators.