[Paper Review] Evolution of entanglement entropy at SU($N$) deconfined quantum critical points

Menghan Song, Jiarui Zhao+5 more|arXiv (Cornell University)|Jul 5, 2023

Quantum Mechanics and Applications11 citations

TL;DR

The paper uses an incremental quantum Monte Carlo approach to study entanglement entropy at SU(N) deconfined quantum critical points across N=2 to N=20, finding a finite critical N_c with unitary conformal fixed points for N≥7 and non-unitary behavior for N≤6, explaining SU(2) pseudocriticality.

ABSTRACT

Over the past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across the condensed matter, quantum field theory, and high-energy physics communities, as it is expected to offer a new paradigm in theory, experiment, and numerical simulations that goes beyond the Landau-Ginzburg-Wilson framework of symmetry breaking and phase transitions. However, the nature of DQCP has been controversial. For instance, in the square-lattice spin-1/2 $J$-$Q$ model, believed to realize the DQCP between Néel and valence bond solid states, conflicting results, such as first-order versus continuous transition, and critical exponents incompatible with conformal bootstrap bounds, have been reported. The enigma of DQCP is exemplified in its anomalous logarithmic subleading contribution in its entanglement entropy (EE), which was discussed in recent studies. In the current work, we demonstrate that similar anomalous logarithmic behavior persists in a class of models analogous to the DQCP. We systematically study the quantum EE of square-lattice SU($N$) DQCP spin models. Based on large-scale quantum Monte Carlo computation of the EE, we show that for a series of $N$ smaller than a critical value, the anomalous logarithmic behavior always exists in the EE, which implies that the previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when $N\ge N_c$ with a finite $N_c$ that we evaluate to lie between $7$ and $8$, the DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory with $N$ complex components.

Motivation & Objective

• Investigate whether SU(N) J1–J2–Q spin models at their deconfined quantum critical points realize unitary conformal fixed points across N.
• Determine how entanglement entropy scaling reflects the presence or absence of unitary CFT descriptions.
• Identify the finite critical flavor number N_c separating continuous DQCPs from weakly first-order behavior.

Proposed method

• Compute second Rényi entanglement entropy S_A^(2) using an incremental QMC algorithm tailored for SU(N) spin models.
• Analyze the corner-induced universal log term s via S_A^(2)(l) = a l − s ln l + c with l the boundary length.
• Partition the system to include four 90-degree corners to extract s and its sign.
• Compare s(N) across N to assess compatibility with unitary CFTs (s ≥ 0 required).
• Relate large-N behavior to Abelian Higgs and CP^{N−1} field theories and fit s(N) to a 1/N expansion form.

Experimental results

Research questions

• RQ1 Does the entanglement entropy scaling at SU(N) DQCPs indicate unitary CFT behavior for varying N?
• RQ2 What is the critical flavor number N_c above which DQCPs are consistent with unitary conformal fixed points?
• RQ3 How does the sign and magnitude of the corner coefficient s(N) evolve with N, and what does it imply about Miransky-like pseudocriticality?
• RQ4 Do large-N field theory expectations (Abelian Higgs / CP^{N−1}) align with numerical entanglement results?

Key findings

• For N ≤ 6, the EE scaling yields a negative log-coefficient s, incompatible with a unitary CFT, indicating non-unitary or non-conformal critical behavior.
• For N ≥ 7, the log-coefficient s is non-negative, allowing a unitary CFT description and indicating a genuine DQCP.
• Finite-size scaling and four-loop RG insights are consistent with a finite N_c ≥ 7 above which a stable critical fixed point exists and describes a continuous transition.
• In the large-N limit, results align with Abelian Higgs / CP^{N−1} predictions, supporting a finite N_c where fixed-point collision leads to unitary criticality for N≥N_c.
• The SU(2) case (N=2) is explained as a result of fixed-point collision and annihilation, yielding pseudocritical behavior rather than a true DQCP.
• The leading corner contribution s(N) fits an expected large-N form with a_s ≈ 0.042(9), supporting a universal entanglement structure across the transition.