4 research outputs found
A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices
e classify the matrix product states having only spin-flip and parity
symmetries, which can be constructed from two dimensional auxiliary matrices.
We show that there are three distinct classes of such states and in each case,
we determine the parent Hamiltonian and the points of possible quantum phase
transitions. For two of the models, the interactions are three-body and for one
the interaction is two-bodyComment: 17 pages, 3 figure
Exact ground states for two new spin-1 quantum chains, new features of matrix product states
We use the matrix product formalism to find exact ground states of two new
spin-1 quantum chains with nearest neighbor interactions. One of the models,
model I, describes a one-parameter family of quantum chains for which the
ground state can be found exactly. In certain limit of the parameter, the
Hamiltonian turns into the interesting case . The other model which we label as model II, corresponds to a
family of solvable three-state vertex models on square two dimensional
lattices. The ground state of this model is highly degenerate and the matrix
product states is a generating state of such degenerate states. The simple
structure of the matrix product state allows us to determine the properties of
degenerate states which are otherwise difficult to determine. For both models
we find exact expressions for correlation functions.Comment: 22 pages, references added, accepted for publication in European
Physics Journal
A new family of matrix product states with Dzyaloshinski-Moriya interactions
We define a new family of matrix product states which are exact ground states
of spin 1/2 Hamiltonians on one dimensional lattices. This class of
Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but
at specified and not arbitrary couplings. We also compute in closed forms the
one and two-point functions and the explicit form of the ground state. The
degeneracy structure of the ground state is also discussed.Comment: 15 pages, 1 figur