The Haldane bosonisation scheme and metallic states of interacting fermions in d spatial dimensions
نویسنده
چکیده
We consider the Haldane bosonisation scheme in d spatial dimensions as applied to a realistic model of interacting fermions in d = 2 and unequivocally demonstrate failure of this scheme in d > 1, specifically in d = 2. In addition to tracing back this failure to its origin, we show that nothing as regards the true metallic state of the model under consideration is known with any degree of certainty.
منابع مشابه
On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials in d dimensions
We demonstrate that the skeleton of the Fermi surface Sf;σ pertaining to a uniform metallic ground state (corresponding to fermions with spin index σ) is determined by the Hartree-Fock contribution Σ σ (k) to the dynamical self-energy Σσ(k; ε). That is to say, in order for k ∈ Sf;σ it is necessary (but for anisotropic ground states in general not sufficient) that the following equation be satis...
متن کاملBosonization and fermion liquids in dimensions greater than one.
We develop and describe new approaches to the problem of interacting Fermions in spatial dimensions greater than one. These approaches are based on generalizations of powerful tools previously applied to problems in one spatial dimension. We begin with a review of one-dimensional interacting Fermions. We then introduce a simplified model in two spatial dimensions to study the role that spin and...
متن کاملBosonisation as the Hubbard Stratonovich Transformation
The problem of strongly correlated electrons in one dimension attracted the attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [8] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [6] (1963) and Mattis and Lieb [7] (1963). Considerable contribution to understanding of the generic propert...
متن کاملKinetic Approach to Fractional Exclusion Statistics
Abstract: We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E 49, 5103 (1994)] as a generalization of the Pauli exclusion principle, which is based on a proper definition of the transition probability between two states, we derive a var...
متن کاملMetallic phase between the Fermi glass and the Wigner crystal in two dimensions
Abstract. For intermediate Coulomb energy to Fermi energy ratios rs, spinless fermions in a two-dimensional random potential form a new quantum phase, different from the Fermi glass (weakly interacting Anderson localized states) and the Wigner crystal (regular array of charges pinned by the disorder). The intermediate phase is characterized by an ordered flow of persistent currents with a typic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008