Duality via Sequential Quantum Circuit in the Topological Holography Formalism

Abstract

Two quantum theories which look different but are secretly describing the same low-energy physics are said to be dual to each other. When realized in the Topological Holography formalism, duality corresponds to changing the gapped boundary condition on the top boundary of a topological field theory, which determines the symmetry of the system, while not affecting the bottom boundary where all the dynamics take place. In this paper, we show that duality in the Topological Holography formalism can be realized with a Sequential Quantum Circuit applied to the top boundary. As a consequence, the Hamiltonians before and after the duality mapping have exactly the same spectrum in the corresponding symmetry sectors, and the entanglement in the corresponding low-energy eigenstates differs by at most an area law term.

22 pages, 10 figures, 5 tables references added

References in corpus (21)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Condensate induced transitions between topologically ordered phases
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Anomalies and gauging of U(1) symmetries
• Sequential Quantum Circuits as Maps between Gapped Phases
• Classifying phases protected by matrix product operator symmetries using matrix product states
• Categories of quantum liquids I
• Topological holography, quantum criticality, and boundary states
• One dimensional gapped quantum phases and enriched fusion categories
• Topological aspects of the critical three-state Potts model
• Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• String Condensations in 3+1D and Lagrangian Algebras
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Categories of quantum liquids II
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries

Cited by in corpus (4)

• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Quantum many-body scarring from Kramers-Wannier duality