Exact zero modes in frustrated spin chains

Natalia Chepiga, University of California at Irvine
Event Date and Time: 
Thu, 2017-10-05 14:00 - 15:00
AMPEL #311
Local Contact: 
Ian Affleck

We will show that the effective coupling between the spin-1/2 edge states of a spin-1 chain of finite length can be continuously tuned by frustration. For the J1J2 model with nearest and next-nearest neighbour antiferromagnetic interactions, we will show that the effective coupling in a chain of length L changes sign N0.38L times in the window 0.28J2/J10.75 where the short-range correlations are incommensurate. This implies that there are N zero modes where the singlet and the triplet are strictly degenerate, i.e. N values of J2/J1 where the spin-1/2 edge states are completely decoupled. We argue that this effect must be generic for all incommensurate phases with localized edge states. In particular, we will discuss the appearance of the exact zero modes in the bilinear-biquadratic spin-1 chain at and beyond the Affleck-Kennedy-Lieb-Tasaki point (Jbiq/J1=1/3). We will also show that the effective coupling between spin-1 edge states can be continuously tuned by the antiferronagnetic next-nearest-neighbour interactions in Haldane spin-2 chain. This implies the existence of points with strictly degenerate singlet, triplet and quintuplet states. A few experimental implications will be briefly discussed.

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