Classification of gapped symmetric phases in onedimensional spin systems
Abstract
Quantum manybody systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are shortrange correlated. Based on the local unitary equivalence relation between shortrangecorrelated states in the same phase, we classify possible quantum phases for onedimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetryprotected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present.
 Publication:

Physical Review B
 Pub Date:
 January 2011
 DOI:
 10.1103/PhysRevB.83.035107
 arXiv:
 arXiv:1008.3745
 Bibcode:
 2011PhRvB..83c5107C
 Keywords:

 75.10.Pq;
 64.70.Tg;
 Spin chain models;
 Quantum phase transitions;
 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 21 pages, 7 figures. Version 2, classification for parity and translation symmetry updated