Sine-square deformation of solvable spin chains and conformal field theories

Abstract

We study solvable spin chains, one-dimensional massless Dirac fermions, and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function $f(x)={\sin }^2(\pi x/\ell )$, where $x$ is the position and $\ell$ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac-Moody) algebras, including $c=1$ Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies.

20pages, 3 figures, new examples and references added, typos corrected

References in corpus (9)

• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Sine-square deformation of free fermion systems in one and higher dimensions
• Boundary effects in the density-matrix renormalization group calculation
• Exact ground state of the sine-square deformed XY spin chain
• Suppression of finite-size effects in one-dimensional correlated systems
• Unconventional Neel and dimer orders in a spin-1/2 frustrated ferromagnetic chain with easy-plane anisotropy
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation
• Quantum state transfer in spin chains with q-deformed interaction terms

Cited by in corpus (50)

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• 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
• Sine-square deformation and Mobius quantization of two-dimensional conformal field theory
• Diffusive Heat Waves in Random Conformal Field Theory
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• "Grand Canonical" Finite Size Numerical Approaches : a Route to Measuring Bulk Properties under Applied Field
• Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Infinite circumference limit of conformal field theory
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Quantum XX-model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• A quantum phase transition in the one-dimensional water chain
• Magnetic susceptibility of quantum spin systems calculated by sine square deformation: one-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets
• Sine-Square Deformation and its Relevance to String Theory
• Zero-energy states in conformal field theory with sine-square deformation
• Quantum information geometry of driven CFTs
• 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
• Conformal Floquet dynamics with a continuous drive protocol
• The Real-Time Correlation Function of Floquet Conformal Fields
• Sine-square deformation and supersymmetric quantum mechanics
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Inhomogeneous XX spin chains and quasi-exactly solvable models
• Thermal and dissipative effects on the heating transition in a driven critical system
• Ground state phase diagram of twisted three-leg spin tube in magnetic field
• Virasoro Entanglement Berry Phases
• Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space
• 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
• Analysis for Lorentzian conformal field theories through sine-square deformation
• Quantum criticality in chains of planar rotors with dipolar interactions
• Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation
• Ground-state phase diagram of the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy under transverse fields
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Long distance entanglement in one-dimensional quantum systems under sinusoidal deformation
• Energy Scale Deformation on Regular Polyhedra
• Perfect Wave Transfer in Continuous Quantum Systems
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices