Entanglement entropy and disorder operator at kagome deconfined quantum criticality

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.

Figures (3)

• Figure 1: (a)Kagome lattice of extended hard-core Boson-Hubbard model: disorder operator $X_M$ and entanglement entropy $S^{(2)}$ are applied on regions $M$ with size $R \times R$ and perimeter $l=4R-4$ in the $L \times L$ lattice. (b) The schematic quantum phase diagram of the EHBHM at $1/3$ filling.
• Figure 2: The second order Rényi entanglement entropy $S_M^{(2)}$ as function of $l$ at the DQCP ($t_c/V=0.130262$) with $\beta=50 L/3$. The fitting result is $S_M^{(2)}(L)=0.8413(3)L-0.108(3)\ln{L}-0.776(3)$. Inset shows the $S_M^{(2)}(L)-aL$ versus $L$ such that the sign of the log-corrections manifest.
• Figure 3: (a) Disorder parameter $|\langle X_M(\theta) \rangle|$ as function of $l$ at the DQCP ($t_c/V=0.130262$) with $\theta=\pi/4, \pi/2, 3\pi/4,\pi$ and system sizes up to $L=72$, $R\in [1,L/2]$. Dots are the QMC results with error bars smaller than the symbol size and the solid lines show the fit by the function in Eq. \ref{['eq:eq3']}. (b) The $\theta$ dependence of universal coefficient $s$ for different system sizes. For small $\theta$, a quadratic dependence clearly manifests. (c) The finite-size results converge for $L$ and fitting with Eq. \ref{['eq:eq6']} yields the coefficient $\frac{s}{f_M\theta^2}\approx 0.0152(5)$, about 1/3 times larger than that of the 3D U(1) where ${C_J}/{(4\pi)^2}=0.01145$.