Nonperturbative Functional Renormalization-Group Approach to the Sine-Gordon Model and the Lukyanov-Zamolodchikov Conjecture

2018/12/05 by Romain Daviet, R. Daviet, N. Dupuis · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Bound state #Combinatorics #Conjecture #Exponential function #Integer (computer science) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Renormalization group #Soliton #cond-mat.stat-mech #hep-th #sine-Gordon equation

paper · pdf · doi:10.1103/physrevlett.122.155301

published as Phys. Rev. Lett. 122, 155301 (2019) · 5+5 pages, 8 figures

arxiv created 2018/12/05 · openalex publication_date 2019/04/19 · arxiv updated 2019/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value ⟨e^(i/2)nβφ⟩ of the exponential fields in the massive phase (n is integer and 2π/β denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.

Citations

• Bosonization and Strongly Correlated Systems
• Exact evolution equation for the effective potential
• Quantum theory of solitons
• Flow Equation Solution for the Weak- to Strong-Coupling Crossover in the Sine-Gordon Model
• Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition
• Quantum inverse problem method. I
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems
• Flow equations forN point functions and bound states
• Kosterlitz-Thouless Phase Transition in the Two Dimensional LinearσModel
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• The nonperturbative functional renormalization group and its applications
• Topological phase transitions in four dimensions