Sylvain Capponi

We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wavefunctions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.

An $S=1$ Haldane chain is a one-dimensional (1D) quantum magnet where strong fluctuations result in quantum disordered singlet ground state with a gapped excitation spectrum. The gap magnitude is primarily set by the dominant intrachain interaction ($J_\text{1D}$). An applied magnetic field closes the gap at $B_\text{c1}$ and drives the system into a gapless Tomonaga-Luttinger liquid (TLL) regime, followed by, at lower temperatures, a Bose-Einstein condensate (BEC) ground state, persisting up to $B_\text{c2} \propto 4 J_\text{1D}/gμ_B$. Almost all previously studied experimental realizations of such systems were based on transition-metal complexes which typically suffer from intrinsic anisotropies or large $J_\text{1D}$ values, limiting the access to the full theoretical phase diagram. We report a comprehensive study of TLL and BEC phases in the organic Haldane chain system 3,5-bis(N-tert-butylaminoxyl)-3'-nitrobiphenyl (BoNO). The absence of anisotropy and a moderate $J_\text{1D}$ enable exploration of the complete $B-T$ phase diagram. Through $^1$H nuclear magnetic resonance, combined with theoretical analysis, we characterize the TLL properties, map the BEC phase boundary $T_c (B)$, determine the associated critical exponent $ν\approx 0.66$ at $B_\text{c2}$, and demonstrate universal quasiparticle scaling in the quantum-critical regime. These results provide full experimental validation of theoretical predictions for field-induced phases in an $S=1$ Haldane chain, made over two decades ago.

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance (NMR) spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the Néel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.