Form factors in finite volume I: form factor bootstrap and truncated conformal space

Abstract

We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.

43 pages, 31 eps figures, LaTeX2e file. v2: main theoretical argument substantially expanded and clarified, typos and references corrected

References in corpus (22)

• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Weak transition matrix elements from finite-volume correlation functions
• On the Operator Content of the Sinh-Gordon Model
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• $K\to \pi \pi$ Decays in a Finite Volume
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• A comment on finite temperature correlations in integrable QFT
• Decay of particles above threshold in the Ising field theory with magnetic field
• Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at $T=T_c$
• Counting the local fields in SG theory.
• The k-folded sine-Gordon model in finite volume
• The space of local operators in perturbed conformal field theories,
• Characterization of resonances using finite size effects
• Form-Factor Bootstrap and the Operator Content of Perturbed Minimal Models
• The form factors in the finite volume
• On the relation between Phi(1,2) and Phi(1,5) perturbed minimal models
• Finite-Volume Form Factors in Semiclassical Approximation
• Universal Amplitude Ratios of The Renormalization Group: Two-Dimensional Tricritical Ising Model
• Vacuum Expectation Values from a variational approach
• One-point functions in integrable quantum field theory at finite temperature

Cited by in corpus (93)

• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Hydrodynamic Diffusion in Integrable Systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Quantum Quenches in Integrable Field Theories
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Quantum quench in the sine-Gordon model
• Dynamics in the Ising field theory after a quantum quench
• Correlation functions and transport coefficients in generalised hydrodynamics
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Form factor expansion for thermal correlators
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Mean values of local operators in highly excited Bethe states
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Structure constants at wrapping order
• Overlaps after quantum quenches in the sine-Gordon model
• Entanglement Content of Quasi-Particle Excitations
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Current operators in integrable models: A review
• String field theory vertex from integrability
• One-point functions in massive integrable QFT with boundaries
• Quench dynamics of the Ising field theory in a magnetic field
• Truncated Hilbert space approach to the 2d ${\varphi }^4$ theory
• Overlap singularity and time evolution in integrable quantum field theory
• Sine-Gordon form factors in finite volume
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Entanglement Content of Quantum Particle Excitations II. Disconnected Regions and Logarithmic Negativity
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Entanglement Content of Quantum Particle Excitations I. Free Field Theory
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Luscher's mu-term and finite volume bootstrap principle for scattering states and form factors
• Truncated Conformal Space Approach for Perturbed Wess-Zumino-Witten $SU(2{)}_k$ Models
• On Form Factors in nested Bethe Ansatz systems
• From the octagon to the SFT vertex - gluing and multiple wrapping
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
• Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
• Kibble-Zurek mechanism in the Ising Field Theory
• Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
• Spectral expansion for finite temperature two-point functions and clustering
• Boundary form factors in finite volume
• Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions
• Form factor perturbation theory from finite volume
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Asymptotic Four Point Functions
• LeClair-Mussardo series for two-point functions in Integrable QFT
• Comments on World-Sheet Form Factors in AdS/CFT
• Diagonal multi-soliton matrix elements in finite volume
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
• Form factor approach to diagonal finite volume matrix elements in Integrable QFT
• Sine-Gordon multi-soliton form factors in finite volume
• Perturbative post-quench overlaps in Quantum Field Theory
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Classical limit of diagonal form factors and HHL correlators
• Entanglement Entropy from the Truncated Conformal Space
• Chirally Factorised Truncated Conformal Space Approach
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Exact finite volume expectation values of local operators in excited states
• One-point functions in finite volume/temperature: a case study
• Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model
• Leading exponential finite size corrections for non-diagonal form factors
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Breather boundary form factors in sine-Gordon theory
• Inelastic decay from integrability
• Field theoretical derivation of Lüscher's formula and calculation of finite volume form factors
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions
• Finite volume form factors in the presence of integrable defects
• Finite temperature expectation values of boundary operators
• Form factors in equilibrium and non-equilibrium mixed states of the Ising model
• Regularization of multi-soliton form factors in sine-Gordon model
• Exact finite volume expectation values of $\bar{\Psi }\Psi$ in the Massive Thirring model from light-cone lattice correlators
• Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
• A study of integrable form factors in massless relativistic AdS_3
• Gluing Hexagons at Three Loops
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model
• Relaxation dynamics of integrable field theories after a global quantum quench
• On the finite volume expectation values of local operators in the sine-Gordon model
• Mesons in a quantum Ising ladder
• TCSA and the finite volume boundary state
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models
• Finite volume form factors in integrable theories
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench
• A diagrammatic approach towards the thermodynamics of integrable systems
• Dynamical correlation functions in the Ising field theory
• Finite volume corrections of non-diagonal form factors
• Norm of Bethe-wave functions in the continuum limit
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory