Recent works on the scaling behaviors of entanglement entropy at the SO(5) deconfined quantum critical point (DQCP) sparked a huge controversy. Different bipartitions gave out totally different conclusions for whether the DQCP is consistent with a unitary conformal field theory. In this Letter, we connect two previously disconnected fields-the many-body entanglement and the surface criticality-to reveal the behaviors of entanglement entropy in various bipartite scenarios, and point out that only the ordinary bipartition purely reflects the criticality of the bulk; otherwise, the extra gapless edge mode will also contribute to the entanglement. We have demonstrated that the correspondence between the entanglement spectrum and the edge energy spectrum still approximately persists even at a bulk-gapless point, thereby influencing the behavior of entanglement entropy. Our results establish that boundary conditions induced by the cut are decisive for entanglement-based probes and provide practical protocols to separate bulk from boundary contributions.
Recent works on the scaling behaviors of entanglement entropy at the SO(5) deconfined quantum critical point (DQCP) sparked a huge controversy. Different bipartitions gave out totally different conclusions for whether the DQCP is consistent with a unitary conformal field theory. In this Letter, we connect two previously disconnected fields-the many-body entanglement and the surface criticality-to reveal the behaviors of entanglement entropy in various bipartite scenarios, and point out that only the ordinary bipartition purely reflects the criticality of the bulk; otherwise, the extra gapless edge mode will also contribute to the entanglement. We have demonstrated that the correspondence between the entanglement spectrum and the edge energy spectrum still approximately persists even at a bulk-gapless point, thereby influencing the behavior of entanglement entropy. Our results establish that boundary conditions induced by the cut are decisive for entanglement-based probes and provide practical protocols to separate bulk from boundary contributions.
Entanglement entropy (EE) is a fundamental probe of quantum phases and critical phenomena, which was thought to reflect only bulk universality for a long time. Very recently, people realized that the microscopic geometry of the entanglement cut can induce distinct entanglement-edge modes, whose coupling to bulk critical fluctuations may alter the scaling of the EE. However, this perception is very qualitative and lacks quantitative consideration. Here, we investigate this problem through high-precision quantum Monte Carlo simulations combined with the analysis of scaling theory to build a quantitative understanding. By considering three distinct bipartitions corresponding to three surface criticality types, we reveal a striking dependence of the constant term γ on the microscopic cut at the quantum critical point. Notably, cuts that generate extra gapless edge modes yield a sign reversal in γ compared to those producing gapped edges. We explain this behavior via a modified scaling form that incorporates contributions from both bulk and surface critical modes. Furthermore, we demonstrate that the derivative of EE robustly extracts the bulk critical point and exponent ν regardless of the cut geometry, providing a reliable diagnostic of bulk universality in the presence of strong surface effects. Our work for the first time establishes a direct quantitative connection between surface criticality and entanglement scaling, challenging the conventional view that EE solely reflects bulk properties and offering a refined framework for interpreting entanglement in systems with boundary-sensitive criticality.
The deconfined quantum critical point (DQCP) in square lattice S=1/2 quantum antiferromagnets has been extensively studied with a large body of evidence pointing to a weakly first-order transition scenario. Recent studies, which focused on entanglement at this nearly continuous DQCP in square lattice J-Q models, have observed conflicting bipartite entanglement entropy (EE) scaling behavior. One bipartition choice gave scaling coefficients in remarkable agreement with predictions from the unitary CFT corresponding to the putative DQCP. While another equally natural choice gave scaling coefficients in complete violation of unitary CFT that may be attributed to lack of scale invariance at the known weakly first-order behavior of the model. This motivates the exploration of DQCP behavior via entanglement measures in lattice models with distinct crystalline symmetries. Here we study a S=1/2 honeycomb model that hosts a nearly continuous transition between Néel and valence-bond-solid ground states relevant to probing DQCP. Using large-scale quantum Monte Carlo simulations, we compute the Rényi EE for a variety of bipartitions and test the CFT based description of the DQCP on the honeycomb lattice. For smooth bipartitions, we find no evidence of logarithmic corrections, in accordance with CFT, thereby essentially ruling out contributions from Goldstone modes. For subsystems with corners, CFT predicts universal logarithmic contributions, which we extract for corners with 60 and 120 degree angles and find close agreement with an emergent SO(5) CFT. While we observe scaling consistent with a critical system in the majority of cases, we also demonstrate an intriguing counterexample of the hexagon subsystem that exhibits a subtle period three oscillation. This results in three separate finite-size series, where the sign of the logarithmic term apparently changes depending on the series.
We study the Rényi entanglement entropy (EE) of the two-dimensional J-Q model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum Monte Carlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-N conformal field theory with SO(N=5) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for cornerless bipartitions. We here use a 45° tilted cut on the square lattice. Beyond supporting an SO(5) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.
Over past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across physics communities, as it offers a new paradigm beyond the Landau-Ginzburg-Wilson framework. However, the nature of DQCP has been controversial based on conflicting numeric results. In our work, we demonstrate that an anomalous logarithmic behavior in the entanglement entropy (EE) persists in a class of models analogous to the DQCP. On the basis of quantum Monte Carlo computation of the EE on SU( N ) DQCP spin models, we show that for a series of N smaller than a critical value, the anomalous logarithmic behavior always exists, which implies that previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when N ≥ N c with an N c we evaluate to lie between 7 and 8, DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory.
Entanglement scaling provides a powerful probe of universal properties at quantum critical points. In two dimensions, contributions originating from a corner-shaped bipartition exhibit a universal scaling, which is determined by the underlying conformal field theory. We develop a method to extract this corner entanglement entropy from projected entangled pair states directly in the thermodynamic limit. When applied to models at a quantum critical point, we show that the corner contribution exhibits scaling with the effective correlation length, in agreement with the hypothesis of finite-entanglement scaling. Our results for the corner coefficients are consistent with other methods, demonstrating the efficiency of our method for diagnosing strongly-correlated quantum critical points in two dimensions.
Generally speaking, entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short-range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in long-range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Furthermore, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. In this work, we simultaneously explore the geometric and edge contributions in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Their scaling is found to be consistent with conformal field theory (CFT) predictions and recent results of particle number fluctuation calculations.