Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representationLi-Xiang Cen1 and Z. D. Wang2
1 Department of Physics, Sichuan University - Chengdu 610065, China
2 Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong Pokfulam Road, Hong Kong, China
received 4 January 2008; accepted in final form 26 March 2008; published May 2008
published online 7 May 2008
The property of quantum many-body systems under spatial reflection and the relevant physics of the renormalization group (RG) procedure are revealed. By virtue of the matrix product state (MPS) representation, various attributes for translational invariant systems associated with spatial reflection are manifested. We demonstrate subsequently a conservation rule of the conjugative relation for reflectional MPS pairs under RG transformations and illustrate further the property of the fixed points of RG flows. Finally, we show that a similar rule exists with respect to the target states in the density matrix renormalization group algorithm.
05.10.Cc - Renormalization group methods.
75.10.Jm - Quantized spin models.
02.70.-c - Computational techniques; simulations.
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