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Automorphic equivalence of gapped ground states and the classification of gapped phases
Mathematical Physics| Speaker: | Bruno Nachtergaele, UCDavis, Math. Dept |
| Location: | 2112 MSB |
| Start time: | Tue, Jan 31 2012, 12:00AM |
Description
I will discuss the flow of automorphisms connecting ground states of model
Hamiltonians belonging to the same gapped ground state phase. To illustrate
how the notion of automorphic equivalence provides a useful classification of
gapped ground state phases, I introduce a family of quantum spin chains with
nearest neighbor interactions of which the ground states can be described as
a product vacuum with a finite number of particles bound to the edges. The
numbers of particles, n_L and n_R, that can bind to the left and right edges of
the finite chains serve as indices of the particular phase a model belongs to.
All these ground states, which we called Product Vacua with Boundary States
(PVBS) can be described as Matrix Product States (MPS). As an example I
present a curve of Hamiltonians connecting the AKLT model to its representative
PVBS model, which has indices n_L=n_R=1.
(joint work with Sven Bachmann, Spyridon Michalakis, and Robert Sims)