2002/07/02 by Gerardo Ortíz, G. Ortiz, Cristian D. Batista +1 · 9 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian (control theory) #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Quantum statistical mechanics #Statistical mechanics #Statistical physics #Superfluidity #Theoretical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.67.134301
published in Physical review. B, Condensed matter 67(13) (American Physical Society) · 4 pages, 2 psfigures. submitted Phys. Rev. B
arxiv created 2002/07/02 · openalex publication_date 2003/04/04 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian, modeling the system, can always be written in a hierarchical operator language that unveils all symmetry generators of the problem and, thus, possible thermodynamic phases. In general, one cannot compute the thermodynamic or zero-temperature properties exactly and an approximate scheme named ``hierarchical mean-field approach'' is introduced. This approach treats all possible competing orders on an equal footing. We illustrate the methodology by determining the phase diagram and quantum critical point of a bosonic lattice model which displays coexistence and competition between antiferromagnetism and superfluidity.