2014/09/30 by Andrea Coser, Marco Beria, Giuseppe Piero Brandino +3 · 1 citation
Mathematics · Physics and Astronomy · #Boson #Bound state #Cold Atom Physics and Bose-Einstein Condensates #Conformal map #Landau theory #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Parameter space #Perturbation theory (quantum mechanics) #Phase space #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum mechanics #Semiclassical physics #Space (punctuation) #Spectrum (functional analysis) #Theoretical physics #Upper and lower bounds #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.1088/1742-5468/2014/12/p12010
published as J. Stat. Mech. (2014) P12010 · 29 pages, 12 figures, v2: added discussion about the parameter beta, added references, other minor changes, published version
openalex publication_date 2014/12/10 · arxiv created 2014/12/20 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the spectrum of Landau–Ginzburg theories in 1 + 1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a Φ 2 theory (i.e. a free massive boson) in this framework. We then turn to Φ 4 in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of Φ 4 where kink excitations together with their bound states are present. We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of Φ 6 Landau–Ginzburg theory, again finding agreement.