Regensburg 2013 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 14: Correlated Electrons: Low-Dimensional Systems - Models 2

TT 14.14: Vortrag

Montag, 11. März 2013, 18:30–18:45, H9

Topological phases of spin chains — Kasper Duivenvoorden and •Thomas Quella — Universität zu Köln, Institut für Theoretische Physik, Köln, Deutschland

The Haldane phase of one-dimensional S=1 spin chains with SU(2) symmetry is one of the first topological states of matter. In particular, it features a bulk-boundary correspondence, with S=1/2 degrees of freedom emerging at the boundaries of the system. Moreover, it exhibits a diluted anti-ferromagnetic order which can be measured using a non-local string order parameter. With the prospect of being able to simulate spin chains with SU(N) symmetry in the laboratory using ultracold earth-alkaline atoms it is a natural and interesting question whether similar topological phases also exist beyond N=2.

In a recent paper we have shown that this is indeed the case. More precisely, spin chains with SU(N) symmetry allow for up to N different topological phases, N−1 of which are topologically non-trivial. These phases exhibit topological order that is reflected in a specific entanglement pattern resulting from the matrix product state representation of the corresponding ground state wave function. It may be detected using a non-local string order parameter which characterizes each of the N phases unambiguously. Analytical and numerical results confirm that our order parameter may be used to extract a quantized topological invariant.