Effective interactions due to quantum fluctuations

Abstract

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.

35 pages, AMSLatex

References in corpus (2)

• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
• Rigidity of interfaces in the Falicov-Kimball model

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• Segregation in the asymmetric Hubbard model
• Quantum spin systems at positive temperature
• Mott transition in lattice boson models
• Quantum lattice models at intermediate temperatures
• Charge Order in the Falicov-Kimball Model
• Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
• Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory
• Falicov-Kimball Models: A Partial Review of the Ground States Problem
• Analyticity in Hubbard models
• Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory
• Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy