Slave-boson fractionalization and polaronic dynamics across the BCS-Mott crossover in single-band Hubbard systems

English Abstract: We investigate an analytical framework bridging the weakly coupled Bardeen-Cooper-Schrieffer (BCS) regime and strongly correlated macroscopic quantum states, with a focus on single-band Mott-Hubbard systems. To address the finite-temperature thermodynamic challenges inherent in standard Gutzwiller projections, we embed the pairing wavefunction within a Slave-Boson Mean-Field Theory (SBMFT). Incorporating a doping-scaled inter-layer coupling to satisfy the Mermin-Wagner restrictions provides a mechanism for finite-temperature holon condensation to remain thermodynamically stable. Subject to the nearest-neighbor pairing boundary condition and the zero-integral constraint dictated by the restricted Hilbert space, we find that the B1g irreducible representation (d-wave) optimizes the ground state energy in the Mott limit. Furthermore, evaluating emergent U(1) gauge fluctuations elucidates the distinction between the Anderson-Higgs gapped superconducting state and the gapless pseudogap phase. By mapping holon dynamics onto the Bardeen-Stephen vortex flow via the Ioffe-Larkin composition rule, we construct a descriptive model for AC microwave dissipation. Selective polaronic dressing of charged holons, driven by anti-adiabatic timescale separation, yields a spatially dependent pinning functional for pancake vortices and a doping-gated isotope coefficient. This Polaronic Fractionalization Model (PFM) provides a consistent perspective on the superconducting dome and captures the qualitative phenomenology of strongly correlated quasi-two-dimensional systems. 中文摘要: 我們探討一個橋接弱耦合 Bardeen-Cooper-Schrieffer (BCS) 區間與強關聯宏觀量子態的解析框架,並聚焦於單帶 Mott-Hubbard 系統。為了處理標準 Gutzwiller 投影中固有的有限溫度熱力學挑戰,我們將配對波函數嵌入奴隸玻色子平均場理論 (SBMFT) 中。透過引入隨摻雜調節的層間耦合以滿足 Mermin-Wagner 限制,為有限溫度下的空穴子 (holon) 凝聚保持熱力學穩定提供了一種機制。在受限希爾伯特空間 (Hilbert space) 所決定的最近鄰配對邊界條件與積分為零約束 (zero-integral constraint) 下,我們發現 B1g 不可約表示 (d波) 在 Mott 極限下能最佳化基態能量。此外,透過評估湧現的 U(1) 規範漲落,闡明了具備 Anderson-Higgs 能隙的超導態與無能隙贗能隙相之間的物理區別。藉由 Ioffe-Larkin 複合規則將空穴子動力學映射至 Bardeen-Stephen 渦旋流,我們建構了一個描述交流微波耗散的模型。由反絕熱 (anti-adiabatic) 時間尺度分離所驅動的帶電空穴子選擇性極化子修飾,產生了適用於餅狀渦旋 (pancake vortices) 的空間相依釘扎泛函 (pinning functional),以及受摻雜調控的同位素係數。此極化子分數化模型 (PFM) 對超導穹頂提供了一致的視角,並捕捉了強關聯準二維系統的定性現象學。