Evolution operators in conformal field theories and conformal mappings: the entanglement Hamiltonian, the sine-square deformation, and others

Abstract

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dxf(x)\mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density of the CFT, and $f(x)$ is an envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian, and the so-called sine-square deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Based on our construction, we also propose a regularized version of the sine-square deformation, which, in contrast to the original sine-square deformation, has the spectrum of the CFT defined on a spatial circle of finite circumference $L$, and for which the level spacing scales as $1/L^2$, once the circumference of the circle and the regularization parameter are suitably adjusted.

arXiv comment11 pages, 16 figures; (v2): The connection between the "square root deformation" and the perfect state transfer is added in v2. We thank Hosho Katsura for pointing out the connection

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Cited by in corpus (50)

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• Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Properties of the entanglement Hamiltonian for finite free-fermion chains
• Emergent Black Hole Dynamics in Critical Floquet Systems
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• Floquet conformal field theories with generally deformed Hamiltonians
• Inhomogeneous conformal field theory out of equilibrium
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• Diffusive Heat Waves in Random Conformal Field Theory
• On the continuum limit of the entanglement Hamiltonian
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Entanglement entropies of inhomogeneous Luttinger liquids
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Deterministic chaos and fractal entropy scaling in Floquet CFT
• Zero-energy states in conformal field theory with sine-square deformation
• Quantum information geometry of driven CFTs
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Conformal Quantum Mechanics and Sine-Square Deformation
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems
• Modular Hamiltonian for (holographic) excited states
• The Real-Time Correlation Function of Floquet Conformal Fields
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• Sine-square deformed mean-field theory
• Sine-square deformation applied to classical Ising models
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• A Simple Mechanism for Unconventional Superconductivity in a Repulsive Fermion Model
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Analysis for Lorentzian conformal field theories through sine-square deformation
• Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation
• Lattice Unruh effect and world-line entanglement for the XXZ chain
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT
• Energy Scale Deformation on Regular Polyhedra
• Perfect Wave Transfer in Continuous Quantum Systems
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain