Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories

Abstract

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 ${\Phi }^2$ theory (i.e. a free massive boson) in this framework. We then turn to ${\Phi }^4$ 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 ${\Phi }^4$ 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 ${\Phi }^6$ Landau-Ginzburg theory, again finding agreement.

29 pages, 12 figures, v2: added discussion about the parameter beta, added references, other minor changes, published version

References in corpus (3)

• Excited state TBA and renormalized TCSA in the scaling Potts model
• Neutral Bound States in Kink-like Theories
• The particle spectrum of the Tricritical Ising Model with spin reversal symmetric perturbations

Cited by in corpus (7)

• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Exact finite volume expectation values of local operators in excited states
• The Two-Loop ${\varphi }^4$ Kink Mass