Dynamic mean field theory of the Gutzwiller-projected BCS Hamiltonian: phase fluctuation and pseudogap

D. Ya. Petrina

Kwon Park

One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, $U$, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to $U$.

Kwon Park

The Gutzwiller-projected BCS Hamiltonian is a useful model for high-temperature superconductivity due to its equivalence to the Heisenberg model at half filling and a close connection to the t – J model at moderate doping. In this work, a dynamical mean field theory (DMFT) is developed for the BCS Hamiltonian with d-wave pairing subject to on-site repulsive interaction, U , which we call the BCS+ U model. The large- U limit corresponds to the Gutzwiller-projected BCS Hamiltonian. It is shown that the equivalence between the Heisenberg and the Gutzwiller-projected BCS model is a manifestation of a broader duality in the BCS+ U model: for any finite U , the local dynamics of the BCS+ U model is dual at half filling with respect to the exchange between the hopping parameter, t , and the pairing amplitude, Δ. It is explicitly demonstrated in our DMFT analysis that the real superconducting gap, determined from the sharp coherence peaks in the local density of states, shows strong renormalization from its bare value as a function of U .

Ting-Kuo Lee, Chung-Pin Chou, Fan Yang

Hsinchuan Lin

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。

Giang H. Bach