Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Following the pioneering works with the fuzzy sphere methods [W. Zhu, et al, Phys. Rev. X 13, 021009], we apply the spherical Landau level regularization to study the effective (2+1)D SO(5) non-linear sigma model with a topological term and the potential DQCP therein. Utilizing the state-of-the-art density matrix renormalization group method with explicit $\text{SU(2)}_\text{spin}\times\text{U(1)}_\text{charge}\times\text{U(1)}_\text{angular-momentum}$ symmetry as well as exact diagonalization simulations, we provide a comprehensive phase diagram for the model with a SO(5) continuous transition line -- extension of the previous identified SO(5) multicritical point [arXiv:2307.05307] -- while tuning interaction length. The state-operator correspondence with the conformal tower structure is used to identify the emergent conformal symmetry with the best scaling dimension of relevant primary fields and they match well with the critical exponents obtained from the crossing point analysis of the correlation ratio. Our results thus further support the rich structure of the phase diagram of the SO(5) model.
Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Following the pioneering works with the fuzzy sphere methods [W. Zhu, et al, Phys. Rev. X 13, 021009], we apply the spherical Landau level regularization to study the effective (2+1)D SO(5) non-linear sigma model with a topological term and the potential DQCP therein. Utilizing the state-of-the-art density matrix renormalization group method with explicit SU(2)spin×U(1)charge×U(1)angular-momentum symmetry as well as exact diagonalization simulations, we provide a comprehensive phase diagram for the model with a SO(5) continuous transition line -- extension of the previous identified SO(5) multicritical point [arXiv:2307.05307] -- while tuning interaction length. The state-operator correspondence with the conformal tower structure is used to identify the emergent conformal symmetry with the best scaling dimension of relevant primary fields and they match well with the critical exponents obtained from the crossing point analysis of the correlation ratio. Our results thus further support the rich structure of the phase diagram of the SO(5) model.
Critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Following pioneering works with the fuzzy sphere methods [Zhu et al., Phys. Rev. X 13, 021009 (2023); Hu et al., Phys. Rev. Lett. 131, 031601 (2023); Han et al., arXiv:2312.04047; Zhou et al., Phys. Rev. X 14, 021044 (2024)], we apply the spherical Landau level regularization to study the effective (2+1)D SO(5) nonlinear sigma model with a topological term and the potential DQCP therein. Utilizing the state-of-the-art density matrix renormalization group method with explicit ${\text{SU(2)}}_{\text{spin}}\ifmmode\times\else\texttimes\fi{}{\text{U(1)}}_{\text{charge}}\ifmmode\times\else\texttimes\fi{}{\text{U(1)}}_{\text{angular-momentum}}$ symmetry as well as exact diagonalization simulations, we provide a comprehensive phase diagram for the model with a SO(5) continuous transition line---extension of the previous identified SO(5) multicritical point [Chen et al., Phys. Rev. Lett. 132, 246503 (2024)]---while tuning interaction length. The state-operator correspondence with the conformal tower structure is used to identify the emergent conformal symmetry with the best scaling dimension of relevant primary fields, and they match well with the critical exponents obtained from the crossing point analysis of the correlation ratio. Our results thus further support the rich structure of the phase diagram of the SO(5) model.
Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Here we apply the spherical Landau level regularization upon the exact (2+1)D SO(5) nonlinear sigma model with a topological term to study the potential DQCP therein. We perform a density matrix renormalization group (DMRG) simulation with SU(2)_{spin}×U(1)_{charge}×U(1)_{angular-momentum} symmetries explicitly implemented. Using crossing point analysis for the critical properties of the DMRG data, accompanied by quantum Monte Carlo simulations, we accurately obtain the comprehensive phase diagram of the model and find various novel quantum phases, including Néel, ferromagnet (FM), valence bond solid (VBS), valley polarized (VP) states and a gapless quantum disordered phase occupying an extended area of the phase diagram. The VBS-disorder and Néel-disorder transitions are continuous with non-Wilson-Fisher exponents. Our results show the VBS and Néel states are separated by either a weakly first-order transition or the disordered region with a multicritical point in between, thus opening up more interesting questions on the two-decade long debate on the nature of the DQCP.
The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry-breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy-sphere regularization to study the SO(5) nonlinear sigma model with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact SO(5) symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way toward its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved SO(5) symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we identify 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favor of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the SO(5) DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice. Published by the American Physical Society 2024
Conformal Operator Flows of the Deconfined Quantum Criticality from SO(5) to O(4)
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 work 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.
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.
We develop an optimized continuous-field quantum Monte Carlo (QMC) algorithm to investigate the projected SO(5) nonlinear sigma model with a Wess-Zumino-Witten term, which describes half-filled Dirac fermions in 2+1 space-time dimensions akin to graphene and Yukawa coupled to a quintuplet of compatible mass terms. Our algorithm reduces the computational complexity to O(βNqNϕ2), yielding a speedup of a factor of Nϕ (the number of magnetic fluxes, i.e., system size) relative to prior works [1-4]. This advance enables us to simulate system sizes up to Nϕ=140 on the torus and Nϕ=59 on the sphere, far exceeding the maximum sizes previously accessed, and to map out the universal phase diagram of the model on both geometries. Most notably, we identify and characterize a critical point that separates an SO(5)-broken ordered phase at small coupling from an SO(5)-symmetric disordered phase at large coupling. The critical point becomes multicritical upon the inclusion of terms that break the SO(5) symmetry down to U(1)×SU(2), relevant for the deconfined phase transition between Néel antiferromagnetic and valence-bond-solid orders in quantum magnets. Our finding of a multicritical point in the phase diagram of the SO(5) nonlinear sigma model with Wess-Zumino-Witten term resolves the long-standing open question of its global structure, and our QMC algorithm opens a new avenue for systematic studies of projected Hamiltonians, ranging from correlated flat bands to fractional quantum (anomalous) Hall systems.