Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases

TL;DR

This paper investigates the transition between Haldane and rung-singlet phases in frustrated mixed-spin ladders, revealing an intermediate bond order wave phase using quantum information tools and numerical methods.

Contribution

It provides evidence for a bond order wave phase between Haldane and rung-singlet phases, using entanglement measures and numerical simulations in frustrated mixed-spin ladders.

Findings

Existence of an intermediate phase with unique entanglement spectrum levels

Long-wavelength modulations indicative of bond order waves

Identification of a new phase bridging Haldane and rung-singlet states

Abstract

In frustrated spin ladders the interplay of frustration and correlations leads to the familiar Haldane (H) and rung-singlet (RS) phases. The nature of the transition between these two phases is still under debate. In this paper we tackle this issue using tools of quantum information theory. We consider frustrated mixed-spin-(1, 1/2) ladders with antiferromagnetic leg, rung and diagonal couplings, and calculate various quantities, such as the entanglement entropy (EE), the Schmidt gap, and the level degeneracy of the entanglement spectrum (ES). We use two numerical techniques, the infinite time-evolving block decimation (iTEBD) and the density matrix renormalization group (DMRG). We demonstrate that there exists an intermediate phase in which the ES levels do not exhibit the characteristic degeneracies of the H and RS phases. To understand the underlying physics in this phase, we investigate short-range spin correlations along legs, rungs and diagonals and show that in this intermediate phase long-wavelength modulations occur, akin to bond order waves.