1998/04/04 by Roman Kotecký, R. Kotecky, Daniel Ueltschi +1 · 24 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Degeneracy (biology) #Diagonal #Geometry #Hubbard model #Lattice (music) #Mathematics #Perturbation (astronomy) #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum fluctuation #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Superconductivity #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1007/s002200050707
published in Communications in Mathematical Physics 206(2), 289-335 (Springer Science+Business Media) · 35 pages, AMSLatex
arxiv created 1998/04/04 · openalex publication_date 1999/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum lattice systems are rigorously studied at low temperatures. When the Hamiltonian of the system consists of a potential (diagonal) term and a - small - off-diagonal matrix containing typically quantum effects, such as a hopping matrix, we show that the latter creates an effective interaction between the particles. In the case that the potential matrix has infinitely many degenerate ground states, some of them may be stabilized by the effective potential. The low temperature phase diagram is thus a small deformation of the zero temperature phase diagram of the diagonal potential and the effective potential. As illustrations we discuss the asymmetric Hubbard model and the hard-core Bose-Hubbard model.