Hamiltonian Flow in Condensed Matter Physics

Domenico Finco

Alessandro Cuccoli, Tognetti, Ruggero Vaia +1 more

Andreas Mielke

Accepted for publication in European Physical Journal Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a new generator for the continuous unitary transformation proposed in this paper one can avoid some of the problems of former applications. General properties of the new generator are derived. It turns out that the new generator is especially useful for Hamiltonians with a banded structure. Two examples, the Lipkin model, and the spin–boson model are discussed in detail. PACS-Numbers: 03.65.-w, 02.70.Hm, 31.15.+q, 21.60.-n 1 E–mail:

Michael Ellis Fisher

The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson's crucial concept of flows and fixed points in a large space of Hamiltonians.

Lucas Backes