Hierarchical mean-field theory in quantum statistical mechanics: A bosonic example

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 13, 2003, Pages

  Ortiz, G ^a   Batista, C D ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; CALCULATION; MATHEMATICAL ANALYSIS; PHASE TRANSITION; PHYSICAL PHENOMENA; QUANTUM MECHANICS; THEORY; THERMODYNAMICS;

EID: 0037763949     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.134301     Document Type: Article

References (22)

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12. We know that for (Formula presented) we can find the exact ground and lowest-energy states of H.5
13. One can add temporal fluctuations through a similar type of dynamical mean field as described in Ref. 13 but in the HL.
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15. If we are looking for solutions which could break the lattice translational symmetry (inhomogeneous), we should consider OP’s (Formula presented) for all possible (Formula presented) vectors. In general, nonlocal OP’s can be derived (starting from our local classification) similarly to what has been done in the literature. For instance, for a quantum (Formula presented) system there are two possible local OP’s: the local magnetization and the local spin-nematic parameters. Therefore, in the case of a quantum spin (Formula presented) glass there will be two types of glasses: One where the local magnetization is frozen at each site and another where the local spin-nematic order is frozen at each site. In other words, there will be two Edwards-Anderson OP’s.
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17. Find a matrix (Formula presented) such that (Formula presented) and T satisfies the paraunitarity condition (Formula presented) with (Formula presented)The necessary and sufficient condition for an Hermitian matrix to be paraunitarily diagonalized (with all diagonal elements positive) is that the matrix be positive definite.
18. In this case the eigenvalues can be determined in closed analytic form (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented)
19. In two space dimensions, (Formula presented) (Formula presented) (Formula presented) and (Formula presented)
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