Barrow Holographic Dark Energy with a Ricci Cutoff in Power-Law $f(Q,L_m)$ Gravity: Late-Time Cosmological Dynamics
We investigate late-time Barrow holographic dark energy (BHDE) with Ricci cutoff in $f(Q,L_m)=Q+\alpha Q^n-2L_m$ gravity. The $Q^n$ term modifies the symmetric-teleparallel geometry, while $\Delta$ deforms holographic energy via entropy-area relation. Linear matter Lagrangian allows separate identification of geometric and holographic effects. Modified Friedmann equations with Ricci-cutoff BHDE yield a closed first-order equation for $E(z)=H(z)/H_0$, solved numerically. The model evolves from matter domination to late-time acceleration. Increasing $n$ makes $w_{\mathrm{DE},0}$ less negative, raises $z_t$, lowers $j_0$; increasing $\Delta$ makes $w_{\mathrm{DE},0}$ and $q_0$ more negative, raises $z_t$ and $j_0$. Calibrating $\mathcal{C}_{B,\mathrm{ref}}$ with $q_{0,\mathrm{ref}}\simeq -0.527$ gives $w_{\mathrm{DE},0}\simeq -1.003$, $z_t\simeq0.442$, $j_0\simeq1.486$. Two-dimensional $(n,\Delta)$ maps show opposite effects on $w_{\mathrm{DE},0}$ but same direction on acceleration onset. We compare expansion histories with 36 cosmic-chronometer measurements ($0.07\leq z\leq1.965$), using DESI covariance and asymmetric error at $z=0.8$. Comparison is conditional for fixed trajectories, without fitting; Hubble statistic varies modestly. Results provide a consistent background realization of Ricci-cutoff BHDE in $f(Q,L_m)$ gravity and motivate future perturbation and multi-probe studies.