1. Exactly solvable models in cold atoms, strongly correlated electron systems,  spin chains, vertex models,  spin ladder compounds. 
2. Haldane exclusion statistics, Tomonaga-Luttinger liquids, quantum criticality and quantum correlation functions. 
3. Quantum algebra, quantum groups, open boundary quantum inverse scattering method, quantum transfer matrix.  

Guan undertook his PhD study at Jilin University during 1995-1998. He graduated from Jilin University with  PhD degree in Theoretical Physics in November, 1998. He was awarded the ``Baogang Education Foundation'' prize from  Baogang Education Commission of P. R. China due to his excellent  research outcomes. He then  undertook   postdoctoral research for 3 years at the Technische Universitat Chemnitz, Germany,   the  Universidade Federal de Sao Carlos, Sao Paulo and the Universidade Federal do Rio Grande do sul, Porto Alegre, Brasil. Since his appointment at ANU in February 2003,  Guan  has been working  in the areas of mathematical physics and exactly solvable models in condensed matter, statistical mechanics,  cold atoms and spin liquids. He  was promoted to Level C Fellow effective from January 2009. Since 2013 he is a professor of physics at Wuhan Institute of Physics and Mathematics, Chinese Academy of Science and holds an adjunct associate professor  position at ANU. 

Guan has held/ holds  several visiting positions: 1) a visiting professor position at Tsinghua University, China for 4 months every year from 2012 to 2014; 2) a visiting scientist position at Ohio State University for 3 months in 2010; 3) a regular  visitor to the Institute of Physics, Chinese Academy of Science, Beijing from 2009 to 2011; 4) visiting professor at  Harvard University (2015),  Los Alamos National Laboratory (2014), Laboratoire de Physique Theorique et Modeles Statistique Universite Paris-Sud XI, France (2014), etc. 

From 2011, Guan is  serving  on the Advisory Panel of  Journal of Physics A.