Building models of topological quantum criticality from pivot Hamiltonians

Abstract

Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension $d>1$. Here, we show how the recently introduced notion of the pivot Hamiltonian -- generating rotations between SPT phases -- facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase. The pivot Hamiltonian generates a $U(1)$ pivot symmetry which helps to stabilize a direct SPT transition. The sign-problem free nature of the model -- with an additional Ising interaction preserving the pivot symmetry -- allows us to obtain the phase diagram using quantum Monte Carlo simulations. We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent $SO(5)$ symmetry. The known anomaly of the latter is made possible by the non-local nature of the $U(1)$ pivot symmetry. Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction. This work illustrates the importance of $U(1)$ pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.

arXiv comment19+6 pages. v2 published version

References in corpus (115)

• "Deconfined" quantum critical points
• Entanglement spectrum of a topological phase in one dimension
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological phases of fermions in one dimension
• Classifying quantum phases using Matrix Product States and PEPS
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Topological Quantum Distillation
• Braiding statistics approach to symmetry-protected topological phases
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Deconfined quantum critical points: symmetries and dualities
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Quantum criticality with two length scales
• Walking, Weak first-order transitions, and Complex CFTs
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Integer quantum Hall effect for bosons: A physical realization
• Scaling in the Fan of an Unconventional Quantum Critical Point
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• The Fracton Gauge Principle
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Quantum Hypergraph States
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Fractal symmetries: Ungauging the cubic code
• Comments on Abelian Higgs Models and Persistent Order
• Foliated fracton order from gauging subsystem symmetries
• Intrinsic and emergent anomalies at deconfined critical points
• Topological phases with generalized global symmetries
• Gapless topological phases and symmetry-enriched quantum criticality
• Topology and edge modes in quantum critical chains
• Unfolding the color code
• Intrinsically Gapless Topological Phases
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Gapless Symmetry Protected Topological Order
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Quantum phase transition between cluster and antiferromagnetic states
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Duality between $(2+1)d$ Quantum Critical Points
• The Bond-Algebraic Approach to Dualities
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Scaling of entanglement entropy at deconfined quantum criticality
• Topological Luttinger Liquids from Decorated Domain Walls
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Topological color code and symmetry-protected topological phases
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Symmetric Fracton Matter: Twisted and Enriched
• Deconfined quantum critical point in one dimension
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Structure of 2D Topological Stabilizer Codes
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Cheshire charge in (3+1)-D topological phases
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Twisted foliated fracton phases
• Scaling of disorder operator at deconfined quantum criticality
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Numerical study of a transition between Z2 topologically ordered phases
• Pivot Hamiltonians as generators of symmetry and entanglement
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Ungauging quantum error-correcting codes
• The phase transitions between $Z_n\times Z_n$ bosonic topological phases in 1+1 D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases
• Consistent scaling exponents at the deconfined quantum-critical point
• Symmetry-protected sign problem and magic in quantum phases of matter
• Deconfined Quantum Critical Point on the Triangular Lattice
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• How Quantum Are Non-Negative Wavefunctions?
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Searching for Fracton Orders via Symmetry Defect Condensation
• Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Comment on "Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain"
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
• Intrinsic sign problems in topological quantum field theories
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• One-dimensional model for deconfined criticality with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry
• Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization
• Stochastic Series Expansion Methods
• Continuous phase transition between Neel and valence bond solid phases in a J-Q-like spin ladder system
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy
• Continuous phase transition between bosonic integer quantum Hall liquid and trivial insulator: evidences for deconfined quantum criticality
• Fractonic critical point proximate to a higher-order topological insulator: How does UV blend with IR?
• Fractonic order and emergent fermionic gauge theory
• A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States
• Systematic Constructions of Fracton Theories
• Unconventional quantum phase transitions in a one-dimensional Lieb-Schultz-Mattis system
• Fracton Critical Point in Higher-Order Topological Phase Transition

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• Pivot Hamiltonians as generators of symmetry and entanglement
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• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
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• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
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