Anomalous domain wall condensation in a modified Ising chain

Abstract

We construct a one-dimensional local spin Hamiltonian with an intrinsically non-local, and therefore anomalous, global ${\mathbb{Z}}_2$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and contains a parameter that can be tuned to spontaneously break the non-local ${\mathbb{Z}}_2$ symmetry. The Hamiltonian is constructed to capture the unconventional properties of the domain walls in the symmetry broken phase. Using uniform matrix product states, we obtain the phase diagram that results from condensing the domain walls. We find that the complete phase diagram includes a gapless phase that is separated from the ordered ferromagnetic phase by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered antiferromagnetic phase by a first order phase transition.

arXiv commentPublished version

References in corpus (58)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• "Deconfined" quantum critical points
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Lieb-Schultz-Mattis in Higher Dimensions
• Braiding statistics approach to symmetry-protected topological phases
• 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
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Interacting anyons in topological quantum liquids: The golden chain
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Deconfined quantum critical points: symmetries and dualities
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Scaling of entanglement support for Matrix Product States
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Topological phases with parafermions: theory and blueprints
• Variational optimization algorithms for uniform matrix product states
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Intrinsic and emergent anomalies at deconfined critical points
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Variational matrix product ansatz for dispersion relations
• Deconfined quantum criticality and Neel order via dimer disorder
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Wave Function and Strange Correlator of Short Range Entangled states
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Shadows of Anyons
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Constraints on topological order in Mott Insulators
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Criticality in Translation-Invariant Parafermion Chains
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Chiral symmetry on the edge of 2D symmetry protected topological phases
• Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Anomalies and entanglement renormalization
• Symmetry-protected many-body Aharonov-Bohm effect
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Gapped symmetric edges of symmetry protected topological phases
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Global anomaly detection in two-dimensional symmetry-protected topological phases

Cited by in corpus (5)

• Classifying phases protected by matrix product operator symmetries using matrix product states
• Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation
• Intermediate symmetric construction of transformation between anyon and Gentile statistics
• Fractional domain wall statistics in spin chains with anomalous symmetries
• Les Houches Lecture Notes on Tensor Networks