arXiv:1105.0994 · Physical Review A

Classification of matrix-product ground states corresponding to one-dimensional chains of two-state sites of nearest neighbor interactions

Amir H. Fatollahi, Mohammad Khorrami, Ahmad Shariati, Amir Aghamohammadi

Published Apr 26, 2011• 2 citations

Abstract

A complete classification is given for one-dimensional chains with nearest-neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.

DOI: 10.1103/physreva.83.042108

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arXiv:1105.0994 · Physical Review A

Classification of matrix-product ground states corresponding to one-dimensional chains of two-state sites of nearest neighbor interactions

Amir H. Fatollahi, Mohammad Khorrami, Ahmad Shariati, Amir Aghamohammadi

Published Apr 26, 2011• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.83.042108

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{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 call product vacua with boundary states (PVBS), can be described as matrix product states (MPS). We present a curve of gapped Hamiltonians connecting the Affleck-Kennedy-Lieb-Tasaki (AKLT) model to its representative PVBS model, which has indices

{n}_{L}={n}_{R}=1

. We also present examples with

{n}_{L}={n}_{R}=J

, for any integer $J\ensuremath{\ge}1$, that are related to a recently introduced class of

\text{SO}(2J+1)

-invariant quantum spin chains.

S=5

. We obtain two classes of solutions. One of them converges to the fixed points of renormalization group and the ground states are matrix-product states. Another one does not have renormalization fixed points and the ground states are partially ferromagnetic states.

The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling

J

are studied as functions of temperature and

J

. The two concurrences exhibit a different dependence on

J

at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.