Entanglement Structure of Deconfined Quantum Critical Points

TL;DR

This paper demonstrates that deconfined quantum critical points in 2+1D exhibit richer entanglement structures than conventional critical points, with universal subleading terms in the entanglement entropy encoding topological contributions from emergent gauge fields. Using exact wavefunction constructions for XY* and a partition-function framework, the authors show that the universal β at XY* equals the sum of the XY critical β and the Z2 topological term, and that similar decompositions hold for non-compact CP^1 transitions. They further analyze region-shape dependencies, propose robust subtraction schemes to isolate topological entanglement, and discuss RG-flow implications via an entanglement c-theorem-inspired perspective. Numerical considerations and prior simulations are reviewed, highlighting challenges in extracting universal terms in gapless, deconfined critical systems and outlining directions for future study of entanglement at higher-dimensional quantum critical points.

Abstract

We study the entanglement properties of deconfined quantum critical points. We show not only that these critical points may be distinguished by their entanglement structure but also that they are in general more highly entangled that conventional critical points. We primarily focus on computations of the entanglement entropy of deconfined critical points in 2+1 dimensions, drawing connections to topological entanglement entropy and a recent conjecture on the monotonicity under RG flow of universal terms in the entanglement entropy. We also consider in some detail a variety of issues surrounding the extraction of universal terms in the entanglement entropy. Finally, we compare some of our results to recent numerical simulations.

Figures (4)

• Figure 1: Schematic of the computation of $\hbox{tr}(\rho^2_1)$ illustrating the different connectivities in $R_1$ and $R_2$. Vertical bonds represent contractions of physical degrees of freedom.
• Figure 2: Four regions defining the Levin-Wen procedure for extracting the topological entanglement entropy. The regions are chosen so that all boundary and corner terms will cancel.
• Figure 3: A smoothed version of the annulus entering the Levin-Wen protocol. We need the structure of the reduced density matrix of this geometry as a function of the radii $a$ and $b$.
• Figure 4: Visualizing the modular transformation that maps two copies of the solid torus $B^2 \times S^1$ to the pair of interlocking solid tori on the right. Expanding the interlocking tori to fill all of space and gluing them along their mutual boundary produces $S^3$.