Quantum phase transitions in multileg spin ladders with ring exchange

TL;DR

This paper explores how cyclic four-spin exchange interactions induce exotic phase transitions in multileg spin ladders, revealing new quantum critical behaviors described by conformal field theory and confirmed through numerical methods.

Contribution

It demonstrates that ring exchange interactions can cause novel dimerization phases and quantum phase transitions in N-leg spin ladders, linking these phenomena to SU(2)_N conformal field theory.

Findings

Ring exchange induces staggered or uniform dimerization.

Quantum phase transition described by SU(2)_N conformal field theory.

Numerical confirmation via Exact Diagonalization and DMRG for N ≤ 4.

Abstract

Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general N-leg spin ladder. We show by means of a low-energy approach that, depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)_N conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of Exact Diagonalization and Density Matrix Renormalization Group approaches for N \le 4.