# "Generalization of the Haldane conjecture to SU(3) chains", Miklos Lajko (EPFL Lausanne)

### Date

2017年9月14日 (木) 14:00

C016, Lab1

### Description

Date: September 14th (Thu)

Time: 14:00-15:00

Venue: C016, Lab1

Speaker: Miklos Lajko, Postdoctoral researcher, EPFL Lausanne

Title: Generalization of the Haldane conjecture to SU(3) chains

Abstract:

About 35 years ago, Haldane's conjecture for Heisenberg spin chains came as a surprise to both the condensed matter and high energy physics communities. Mapping the low energy degrees of freedom in the large-S limit to the 1+1 dimensional O(3) nonlinear sigma model with a nontrivial topological term, Haldane argued that integer and half-integer chains have qualitatively different behaviours: while half-integer spin chains are gapless, integer spin chains are gapped with a unique ground state.

In my talk I will give a short review of Haldane's argument, then I will explain how it can be extended to SU(3) chains in the fully symmetric representation with p boxes in the Young tableau. In this case the low energy degrees of freedom can be mapped into a SU(3)/(U(1) x U(1)) nonlinear sigma model with a topological angle $\theta =2\pi p/3$. I will analyse the phase diagram of this nonlinear sigma model using symmetry considerations and  analytic calculations in the strong coupling limit, complemented by Monte Carlo simulations on lattice systems. I will discuss the relation between the sigma model and the spin chain system arguing that SU(3) spin chains are gapped for $p=3m$ but gapless for $p=3m\pm 1$ (for integer $m$), corresponding to a massless critical point of the sigma model at $\theta =\pm 2\pi /3$.

References: ML, Kyle Wamer, Frederic Mila, Ian Affleck, arXiv:1706.06598

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