One-point functions in finite volume/temperature: a case study

Abstract

We consider finite volume (or equivalently, finite temperature) expectation values of local operators in integrable quantum field theories using a combination of numerical and analytical approaches. It is shown that the truncated conformal space approach, when supplemented with a recently proposed renormalization group, can be sufficiently extended to the low-energy regime that it can be matched with high precision by the low-temperature expansion proposed by Leclair and Mussardo. Besides verifying the consistency of the two descriptions, their combination leads to an evaluation of expectation values which is valid to a very high precision for all volume/temperature scales. As a side result of the investigation, we also discuss some unexpected singularities in the framework recently proposed by Pozsgay and Takács for the description of matrix elements of local operators in finite volume, and show that while some of these singularities are resolved by the inclusion of the class of exponential finite size corrections known as μ-terms, these latter corrections themselves lead to the appearance of new singularities. We point out that a fully consistent description of finite volume matrix elements is expected to be free of singularities, and therefore a more complete and systematic understanding of exponential finite size corrections is necessary.

v1: 29 pages, 10 eps figures. v2: 34 pages. A detailed comparison of the theoretically predicted and numerically computed cutoff dependence is added; notations explained in more details and some explanatory remarks are added; typos corrected

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Cited by in corpus (13)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Hamiltonian truncation approach to quenches in the Ising field theory
• The quantum sine-Gordon model with quantum circuits
• Non-equilibrium time evolution and rephasing in the quantum sine-Gordon model
• Equations of state in generalized hydrodynamics
• Quench dynamics of the Ising field theory in a magnetic field
• Kibble-Zurek mechanism in the Ising Field Theory
• Variations on vacuum decay: the scaling Ising and tricritical Ising field theories
• Exact finite volume expectation values of local operators in excited states
• Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Finite volume form factors in the presence of integrable defects
• Inhomogeneous quantum quenches in the sine-Gordon theory