Matrix product states in spin ladders and chains

This talk would be about how MPS formalism through quantum information approach
would help constructing some interesting spin models. These models are:

Spin Ladders
We introduce general classes of ladders of spin-½ particles possessing both discrete and
continuous symmetries. We investigate quantum phase transitions and the behavior of
the entanglement between different neighboring sites near the transition point and will
see that the quantum phase transitions in these models are accompanied by divergence
in derivatives of the entanglement.

Heisenberg Chain
On a particular 2D hypersurface in parameter space of coupling constants, we show that
the Heisenberg spin chain in an external magnetic field is exactly solvable, the ground
state and all the correlation functions can be exactly determined in compact form. This
ground state has a very interesting property: any pairs of spins on the chain are equally
entangled. This might be of much interest for engineering long-rang entanglement in
experimentally realizable finite arrays of qubits.

Generalized Majumdar – Ghosh Chain
We define a multi-parameter family of spin chains, with nearest- and next-nearest-
neighbor interactions. The Majumdar-Ghosh model is a particular point in the parameter
space. The model might also be represented as a zigzag ladder in which triangular 3-
particle couplings also exist. The corresponding ground states of the model are doubly
degenerate and have very simple
Structure being the product of entangled (dimer) states on adjacent sites of the chain or
consecutive rungs of the zigzag ladder.

The talk is based on the following papers:

- M. Asoudeh, V. Karimipour, and A. Sadrolashrafi, Quantum Phase Transitions and
Matrix Product States in Spin Ladders, quant-ph/0612207; to appear in Physical
Review B.

- M. Asoudeh, V. Karimipour, and A. Sadrolashrafi, Exact Ground States for a
Two-Parameter Family of Spin-1/2 XYZ Heisenberg Chains, quant-ph/0701160; to
appear in Physical Review A.

- M. Asoudeh, V. Karimipour, and A. Sadrolashrafi, Exact Dimer Ground States for
a Continuous Family of Quantum Spin Chains and Zigzag Ladders, quant-
ph/0705.0261; to appear in Physical Review B.