Lee-Yang Zeros and Pseudocritical Drift in J-Q Néel-VBS Transitions

Abstract

Square-lattice J-Q models provide a sign-problem-free setting for probing the quantum phase transition between Néel antiferromagnet and columnar valence-bond solid. We analyze this transition through the scaling of Lee-Yang zeros, computed within stochastic series expansion quantum Monte Carlo by reweighting configurations sampled near criticality in the presence of complex source fields. Benchmark studies of the dimerized Heisenberg model and the checkerboard J-Q model validate the method, yielding stable O(3) critical scaling in the former and clear spacetime-volume scaling in the latter, as expected for a first-order transition. Applying the same analysis to the J-Q models, we find a pronounced and systematic drift of the leading-zero scaling with increasing system size, consistent with an extended pseudocritical regime. The Lee-Yang scaling implies an effective scaling dimension of the SO(5) order-parameter field that decreases with size and is consistent with vanishing in the thermodynamic limit. Such behavior lies below the scalar unitarity bound of any unitary relativistic conformal field theory in 2+1 dimensions and enforces inverse spacetime-volume scaling of the zeros, the hallmark of a first-order transition. These results support a weakly first-order interpretation of the Néel-VBS transition and establish finite-size Lee-Yang zeros as a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in the J-Q family.

Figures (4)

• Figure 1: Schematic illustrations of the lattice Hamiltonians studied in this work. (a) Columnar dimerized Heisenberg model with alternating strong and weak nearest-neighbor bonds. (b) Checkerboard J-Q (CBJQ) model with $Q$ interactions on a checkerboard plaquette pattern. (c) Uniform J-Q$_2$ model with $Q_2$ interactions on every plaquette. (d) Uniform J-Q$_3$ model with $Q_3$ interactions on $2\times 3$ and $3\times 2$ rectangles.
• Figure 2: Leading Lee--Yang zeros $g_{\mathrm{LY}}$ and two-size estimators $\eta_{\mathrm{eff}}(L)$ of the $2{+}1$D columnar dimerized Heisenberg model at $J_c=J_2/J_1=1.90951$ma2018anomalous. (a) $-\ln |G|$ along the imaginary-source axis for $L=128$, with red vertical lines marking the leading Lee--Yang zeros. (b) $\eta_{\mathrm{eff}}(L)$ from $(L,2L)$ pairs using the first four zeros. The dashed line shows the $\mathrm{O}(3)$ reference form $\eta+cL^{-\omega}$ with fixed $\eta=0.0375$ and $\omega=0.78$. Inset: leading $g_{\mathrm{LY}}$ versus $1/L$, fitted to $a\,L^{-y_h}\!\left(1+bL^{-\omega}\right)$, with fitted $\eta$ defined by $y_h=(d+z+2-\eta)/2$. The fit uses fixed $\omega=0.78$ and excludes $L\le 32$.
• Figure 3: Leading Lee--Yang zeros $g_{\mathrm{LY}}$ and two-size estimators $\eta_{\mathrm{eff}}(L)$ of the $2{+}1$D CBJQ model at $J_c=J/Q=0.2174$ in panels (a,b), and at $J_c=J/Q=0.2175$zhao2019symmetry in panels (c,d). $\eta_{\mathrm{eff}}(L)$ is obtained from $(L,2L)$ pairs using the first two zeros. The dashed line shows the first-order reference form $\eta+c_1L^{-\omega}+c_2L^{-2\omega}$ with fixed $\eta=-1$. Panels (a,c) show zeros from analytic continuation of the Néel field $h$ conjugate to $M^z$, and panels (b,d) show zeros from analytic continuation of the plaquette-singlet-solid (PSS) source $\eta$ conjugate to $O^{\mathrm{PSS}}$. Insets: leading $g_{\mathrm{LY}}$ versus $1/L$, fitted to $a\,L^{-y_h}$, with fitted $\eta$ defined by $y_h=(d+z+2-\eta)/2$. The fits exclude $L\le 32$.
• Figure 4: Leading Lee--Yang zeros $g_{\mathrm{LY}}$ and two-size estimators $\eta_{\mathrm{eff}}(L)$ of the $2{+}1$D J-Q$_3$ model at $J_c=J/Q_3=0.67045$lou2009antiferromagneticzhao2022scalingtakahashi2024so5 in panels (a,b), and of the $2{+}1$D J-Q$_2$ model at $J_c=J/Q_2=0.045$sandvik2010continuoussuwa2016levelshao2016quantumsandvik2011thermodynamicstakahashi2024so5 in panels (c,d). $\eta_{\mathrm{eff}}(L)$ is obtained from $(L,2L)$ pairs using the first two zeros. The dashed line shows the first-order reference form $\eta+c_1L^{-\omega}+c_2L^{-2\omega}$ with fixed $\eta=-1$. Panels (a,c) show zeros from analytic continuation of the Néel field conjugate to $M^z$, and panels (b,d) show zeros from analytic continuation of the columnar VBS source $\xi_x$ conjugate to $D_x$. Insets: leading $g_{\mathrm{LY}}$ versus $1/L$, fitted to $a\,L^{-y_h}$, with fitted $\eta$ defined by $y_h=(d+z+2-\eta)/2$. The fits exclude $L\le 32$.