Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

Abstract

We propose a new type of quantum liquids, dubbed Stiefel liquids, based on $2+1$ dimensional nonlinear sigma models on target space $SO(N)/SO(4)$, supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of critical quantum liquids with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and $U(1)$ Dirac spin liquid are unified as two special examples of Stiefel liquids, with $N=5$ and $N=6$, respectively. Furthermore, we conjecture that Stiefel liquids with $N>6$ are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of (conventional or parton-like) mean-field construction also means that, within the traditional approaches, it will be difficult to decide whether a non-Lagrangian state can actually emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.

A summary of results can be found on pages 4-6

References in corpus (24)

• "Deconfined" quantum critical points
• Theory of Intertwined Orders in High Temperature Superconductors
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Properties of an algebraic spin liquid on the kagome lattice
• Algebraic spin liquid as the mother of many competing orders
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Coulomb gas transitions in three-dimensional classical dimer models
• Gauge theory picture of an ordering transition in a dimer model
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Majorana liquids: the complete fractionalization of the electron
• Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems
• Trisecting non-Lagrangian theories
• Comparative study of Higgs transition in one-component and two-component lattice superconductor models
• Correlated Fragile Topology: a Parton Approach
• Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models
• Theory of Dirac spin liquids on spin-$S$ triangular lattice: possible application to $\alpha$-CrOOH(D)

Cited by in corpus (32)

• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Scaling of disorder operator at deconfined quantum criticality
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Non-zero momentum requires long-range entanglement
• Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Non-abelian bosonization in two and three spatial dimensions and applications
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Holographic models of non-Fermi liquid metals revisited: an effective field theory approach
• Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
• Classification of symmetry-enriched topological quantum spin liquids
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Classical and quantum spin liquids
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Spin-Peierls instability of deconfined quantum critical points
• Higgs Phases and Boundary Criticality
• Deconfined Quantum Critical Point with Non-locality
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
• Entanglement-enabled symmetry-breaking orders
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• When Wannier centers jump: Critical points between atomic insulating phases