Abstract
This research explores the finite size scaling behavior of Rényi entanglement entropy (EE) in various two-dimensional quantum many-body systems, focusing on the nature of quantum phase transitions, particularly the deconfined quantum critical point (DQCP). We systematically analyze the sub-leading corrections to the EE, employing the “subtracted EE” method to isolate contributions beyond the leading perimeter law. Our findings reveal that for a spin-1/2 model on a square lattice with Néel order, the logarithmic correction coefficient aligns with theoretical predictions based on Goldstone modes. Additionally, we investigate the (2+1)d O(3) Wilson Fisher QCP, where we observe logarithmic corrections at sharp corners but not for smooth boundaries. In the context of DQCP, specifically the square-lattice SU(N) models, we demonstrate that anomalous logarithmic behavior persists for N below a critical threshold, indicating that these transitions do not conform to expected fixed points. For N above this threshold (between 7 and 8), the DQCPs align with conformal fixed points, describable by Abelian Higgs field theories. Our study contributes to the ongoing discourse on DQCPs, highlighting their complex nature and implications for future theoretical and experimental investigations.
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