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arXiv:2606.09985

Bootstrap Cone of the Multicritical Deconfined Quantum Critical Point

Zhijin Li, Tinhong Shen

Published Jun 8, 2026• 0 citations
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Abstract

The deconfined quantum critical point (DQCP) provides a prominent example of the unconventional phase transitions beyond the Landau-Ginzburg-Wilson paradigm and its nature has been controversial for decades. The DQCP has been extensively studied and the results lead to two opposite scenarios with pseudo-criticality or multicriticality. The pseudo-criticality is a prevailing scenario of DQCP which interprets the approximately scale invariant numerical results with the walking behavior near complex fixed points. In contrast, the multicriticality scenario conjectures the DQCP is a unitary fixed point with a relevant $SO(5)$ singlet scalar. In this work we provide substantial evidence for the multicriticality scenario using conformal bootstrap. We start with the observation that the large scale Quantum Monte Carlo (QMC) results nearly saturate the bootstrap bounds. After imposing suitable sparseness condition the bootstrap bound forms a sharp cone in the three-dimensional parameter space. The bootstrap cone is close to the QMC data. We use the navigator algorithm to locate the apex of the cone and extract the extremal solutions. We find striking consistencies between the bootstrap solutions and the fuzzy sphere data of DQCP, including the coefficients in the operator product expansions (OPEs) and the higher spectrum! The bootstrap cone unifies the QMC and the fuzzy sphere data into a unitary conformal field theory with a relevant $SO(5)$ singlet scalar, thus strongly supporting the multicriticality scenario of DQCP. The agreement between the conformal bootstrap, QMC and fuzzy sphere results is a surprise towards solving DQCP and decoding the profound phase diagram of the two-dimensional quantum magnets.

DOI
10.48550/arxiv.2606.09985

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The deconfined quantum critical point (DQCP), which separates two distinct symmetry-broken phases, was conjectured to be an example of (2+1)D criticality beyond the standard Landau-Ginzburg-Wilson paradigm. However, this hypothesis has been met with challenges and remains elusive. Here, we perform a systematic study of a microscopic model realizing the DQCP with a global symmetry tunable from SO(5) to O(4). Through the lens of fuzzy sphere regularization, we uncover the key information on the renormalization group flow of conformal operators. We reveal O(4) primaries decomposed from original SO(5) primaries by tracing conformal operator content and identifying the "avoided level crossing" in the operator flows. In particular, we find that the existence of a scalar operator, in support of the nature of pseudo-criticality, remains relevant, persisting from SO(5) to O(4) DQCP. This Letter not only uncovers the nature of O(4) DQCP but also demonstrates that the fuzzy sphere scheme offers a unique perspective on the renormalization group flow of operators in the study of critical phenomena.
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Deconfined quantum critical point (DQCP) characterizes the continuous transition beyond Landau-Ginzburg-Wilson paradigm, occurring between two phases that exhibit distinct symmetry breaking. The debate over whether genuine DQCP exists in physical SU(2) spin systems or the transition is weakly first-order has persisted for many years. In this letter, we construct a non-Hermitian easy-plane JJJ-QQQ model and perform sign-problem-free quantum Monte Carlo (QMC) simulation to explore the impact of non-Hermitian microscopic interactions on the transition that potentially features a DQCP. Our results demonstrate that the intensity of the first-order transitions significantly diminishes with the amplification of non-Hermitian interactions, serving as numerical evidence to support the notion that the transition in JJJ-QQQ model is quasi-critical, possibly in the vicinity of the fixed point governing DQCP in the complex plane, described by a non-unitary conformal field theory (CFT). The non-Hermitian interaction facilitates the approach towards such a complex fixed point in the parameter regime. Furthermore, our QMC study on the non-Hermitian J-Q model opens a new route to numerically investigating the nature of complex CFT in the microscopic model.
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.