Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories

TL;DR

This paper applies the truncated conformal space approach to 2D Landau-Ginzburg theories, successfully reproducing spectra, validating perturbative predictions, and analyzing kink excitations in broken phases.

Contribution

It demonstrates the effectiveness of the truncated conformal space approach in analyzing 2D Landau-Ginzburg theories across different phases and confirms semiclassical predictions.

Findings

Reproduced the spectrum of free massive boson in $\

Found excellent agreement with two-loop perturbation theory for $\

Confirmed semiclassical predictions for kink-antikink bound states in broken phases.

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.