Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions

TL;DR

This paper analyzes the finite-size spectrum of the critical staggered six-vertex model with antidiagonal boundary conditions, revealing three phases with distinct conformal field theories and complex scaling behaviors.

Contribution

It provides a detailed characterization of the finite-size spectrum under antidiagonal boundary conditions, including explicit formulas for the Q-operator and insights into different critical regimes.

Findings

Three distinct phases identified with different conformal field theories

Logarithmic corrections to ground state scaling under antidiagonal boundary conditions

Explicit Q-operator formula facilitating numerical studies

Abstract

The finite-size spectrum of the critical staggered six-vertex model with antidiagonal boundary conditions is studied. Similar to the case of periodic boundary conditions, we identify three different phases. In two of those, the underlying conformal field theory can be identified to be related to the twisted $U(1)$ Kac-Moody algebra. In contrast, the finite size scaling in the third regime, whose critical behaviour with the (quasi-)periodic BCs is related to the 2d black hole CFTs possessing a non-compact degree of freedom, is more subtle. Here with antidiagonal BCs imposed, the corrections to the scaling of the ground state grow logarithmically with the system size, while the energy gaps appear to close logarithmically. Moreover, we obtain an explicit formula for the Q-operator which is useful for numerical implementation.