Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

TL;DR

This paper investigates the critical properties of quantum three- and four-state Potts models with boundary conditions polarized along the transverse field, revealing conformal invariance and dualities through energy spectrum analysis.

Contribution

It demonstrates the emergence of conformal towers under polarized boundaries and establishes dualities between different boundary conditions in quantum Potts models.

Findings

Boundaries polarized in the transverse field produce scale-invariant conformal towers.

Duality between transverse-polarized and three-state-mixed boundary conditions is phenomenologically established.

New boundary conditions in the three-state Potts model can be realized by polarizing edge spins along the transverse field.

Abstract

By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.