Fidelity between partial states as a signature of quantum phase transitions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 5, 2008, Pages

  Paunkovic N ^a   Sacramento, P D ^b   Nogueira, P ^b   Vieira, V R ^b   Dugaev, V K ^b,c  

^a INSTITUTO DE TELECOMUNICAÇÕES   (Portugal)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^c RZESZOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; MAGNETIZATION; PHASE TRANSITIONS; QUANTUM THEORY; SUPERCONDUCTING MATERIALS;

QUANTUM PHASE TRANSITION; SUPERCONDUCTING LATTICE; UHLMANN MIXED STATE;

ELECTRON ENERGY LEVELS;

EID: 43049101657     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.052302     Document Type: Article

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45. Note that in the case of pure states, this corresponds to the case of mutually orthogonal state vectors.
46. The particular numerical value for δJ was chosen such that the effect of the fidelity drop becomes observable. Alternatively, a more formal approach could be taken, involving the study of a metric tensor, a local quantity induced by the global distance based on the notion of fidelity (see, for example, where the Bures metric was studied).
47. These interaction terms are easily expressed in terms of the electron spin operators S and the Nambu operators T, discussed in detail in. They commute with each other, i.e., [T α, S β] =0, for every α,β { 0,+,- }, and they have a common eigenbasis. In fact, these operators satisfy T α S β =0, and act nontrivially in mutually orthogonal subspaces, with even and odd number of particle occupation numbers, respectively, annihilating the states in the other subspace.