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arXiv:2601.13774

Entanglement entropy and disorder operator at kagome deconfined quantum criticality

Yan-Cheng Wang, Yan Zheng, Xue-Feng Zhang

Published Jan 20, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the deconfined quantum critical point (DQCP) candidate in the extended hard-core Bose-Hubbard model on the kagome lattice, employing quantum Monte Carlo simulations to study the entanglement entropy and the $U(1)$ disorder operator. In stark contrast to findings in $J$-$Q$ models and other candidates, the universal logarithmic correction coefficients for both quantities are found to be {positive}, consistent with a unitary conformal field theory (CFT). Crucially, the current central charge $C_J$, extracted from the small-angle behavior of the disorder operator, is enhanced by a factor of approximately {4/3} compared to that of the conventional 3D $O(2)$ Wilson-Fisher fixed point. This enhancement {implies} a consistent explanation in the recently observed low-energy excitation spectrum at this DQCP, which features {two distinct linearly dispersing modes} with a velocity ratio of approximately three. Our results provide evidence that this quantum phase transition constitutes a genuine DQCP, characterized by coexisting fractionalized excitations that collectively modify its critical properties.

DOI
10.48550/arxiv.2601.13774

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We investigate the deconfined quantum critical point (DQCP) candidate in the extended hard-core Bose-Hubbard model on the kagome lattice, employing quantum Monte Carlo simulations to study the entanglement entropy and the U(1)U(1)U(1) disorder operator. In stark contrast to findings in JJJ-QQQ models and other candidates, the universal logarithmic correction coefficients for both quantities are found to be {positive}, consistent with a unitary conformal field theory (CFT). Crucially, the current central charge CJC_JCJ​, extracted from the small-angle behavior of the disorder operator, is enhanced by a factor of approximately {4/3} compared to that of the conventional 3D O(2)O(2)O(2) Wilson-Fisher fixed point. This enhancement {implies} a consistent explanation in the recently observed low-energy excitation spectrum at this DQCP, which features {two distinct linearly dispersing modes} with a velocity ratio of approximately three. Our results provide evidence that this quantum phase transition constitutes a genuine DQCP, characterized by coexisting fractionalized excitations that collectively modify its critical properties.
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.
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.
The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole-free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.
We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that, at a conformally invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections, and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where we still observe similar scaling behavior, but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with the positivity condition of the Rényi entanglement entropy, which holds for unitary conformal field theories (CFTs). Our results unambiguously reveal fundamental differences between DQC and quantum critical points described by unitary CFTs.
A deconfined quantum phase transition (DQPT) provides an extraordinary possibility of the quantum phase transition beyond the Ginzburg-Landau paradigm, which is interwoven with numerous exotic phenomena of the strongly correlated quantum many-body system, e.g., fractional excitation, emergent symmetries, and gauge field. However, various candidates of DQPT have been demonstrated to be weakly first order, and the conformal field theory has to be altered into a nonunitary one. Here we numerically found two linear dispersions with different velocities in one of the few survivors of DQPT---the extended hard-core Bose-Hubbard model on the kagome lattice. Such counterintuitive results directly lead to the negation of possible emergent Lorentz symmetry and the breakdown of conventional theory of DQPT. Furthermore, the snapshots of boson configuration hint that these two velocities may correspond to the dynamics of the fractional excitations and quantum strings, respectively. Our work will inspire researchers to revisit the theory of DQPT and benefit the field of quantum materials and quantum simulations.
The deconfined quantum critical point (DQCP) -- the enigmatic incarnation of the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm of symmetries and their spontaneous breaking -- has been proposed and actively pursued for more than two decades. Various 2D quantum many-body lattice models, both in spin/boson and fermion representations have been tested with the state-of-the-art numerical techniques and field-theoretical analyses, and yet, the conclusion is still controversial. Experimental realizations of DQCP in the quantum magnet SrCu2_22​(BO3_33​)2_22​ and superconducting quantum criticality in 2D material have either shown first order transition or intermediate phase. The tension between the lattice scale details and the requirement from continuum limit, manifested in the form of the inconsistent critical scaling behavior and violations of generic conformal bootstrap bound, has not been resolved. Here we solve these decades-long controversies from the new and fundamental perspective of the quantum entanglement. We develop the incremental algorithm to compute the entanglement entropy at a fermionic DQCP with unprecedentedly accurate data and reveal the universal coefficient of the logarithmic correction therein is negative and at odds with positivity requirement of the conformal field theory. Together with results in other 2D DQCP lattice models (both in fermion and spin systems), our discoveries clearly demonstrate the 2D SU(2) antiferromagnet to valence bond solid DQCPs are not conformal fixed point and naturally explain the experimental difficulties in finding them. This marks the end of the beginning of unambiguous finding of the quantum phase transitions truely beyond the Landau-Ginzburg-Wilson paradigm, since its suggestion two decades ago.