Competing and Intertwined Orders in Boson-Doped Mott Antiferromagnets

Abstract

Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic $t$-$t'$-$J$ model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level $δ$ and hopping ratio $t'/t$, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave (PDW) phase at low doping and small $|t'/t|$, which is suppressed on the $t'<0$ side, resulting in a disordered PDW state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form a SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the $t'>0$ side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF + $xy$-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of $t'/t$ in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-$T_c$ superconductivity, reflecting the frustrated interplay between doped holes and spin background.

Figures (24)

• Figure 1: Phase diagram and Rydberg experimental scheme. (a) Phase diagram of the bosonic $t$-$t'$-$J$ model on four-leg cylinder. Within $-0.3 \le t' /t \le 0.3$ and $1/24\le \delta \le1/3$, we identify a phase separation (PS) and a SF+$xy$-ferromagnetic (FM) phase on the $t' \ge 0$ side; a SF+AFM phase and a SF*+incommensurate magnetism (IM) phase on the $t' \le 0$ side; a PDW+AFM phase and a dPDW+AFM phase sandwiched by SF+AFM and SF*+IM phases; a bond order wave (BOW) state at the special $\delta=1/4$. The symbols denote the calculated parameter points. (b) The $t$-$t'$-$J$ model with hard-core bosonic holes can be implemented in three Rydberg levels. The tunneling term arises from dipole-dipole exchange interactions between $|S\rangle$ and $|P\rangle$ states. Without affecting the spin interactions, we have a freedom in choosing the magnetic sublevel of the $|P\rangle$ state (hole state) allowing one to implement both signs of tunneling $t'/t$ after a gauge transformation.
• Figure 2: Momentum distribution $n(\bf k)$. (a) dPDW+AFM phase, (b) SF*+IM phase, (c) SF+FM phase, (d) SF+AFM phase, (e) PDW+AFM phase, and (f) PS. Here all the $n(\bf k)$ are obtained by taking the Fourier transformation for the all-to-all single-boson correlations.
• Figure 3: Spin structure factor $S(\bf k)$. (a) dPDW+AFM phase, (b) SF*+IM phase, (c) SF+FM phase, (d) SF+AFM phase, (e) PDW+AFM phase, and (f) PS. Here all the $S(\bf k)$ are obtained by taking the Fourier transformation for the all-to-all spin correlations.
• Figure 4: Pairing and single-boson correlations. (a) and (b) are the double-logarithmic plot of the pairing correlations $P_{yy}(r)$ and the product of two single-boson correlations $G_\sigma^2(r)$ in the PDW+AFM and dPDW+AFM phases, respectively. The power exponents $K_{\mathrm{sc}}$ are obtained by algebraic fitting with dash line. (c) and (d) are the semi-logarithmic plot of the $P_{yy}(r)$ and $G_\sigma^2(r)$ in the SF+AFM and SF*+IM phases, respectively. The correlation lengths $\xi_{\mathrm{sc}}$ are obtained by exponential fitting with dash line. The insets in (a) and (b) show the corresponding pairing structure factor $P_{yy}(k_x)$, where a singular peak or broad dome appears at $\mathbf{Q}_p=\pi$.
• Figure 5: Momentum distribution $n({\bf k})$ and spin structure factor $S({\bf k})$ in the SF*+IM phase on eight-leg systems. (a) and (b) are $n(\bf k)$ at system length $L_{x}=12$ and $24$ for $t'/t=0$, $\delta=1/4$. (c) $S(\bf k)$ at $L_{x}=24$ for $t'/t=0$, $\delta=1/4$. $n(\bf k)$ and $S(\bf k)$ are obtained by taking the Fourier transformation for the all-to-all correlations.