Magnetic and superconducting instabilities in the two-dimensional
t-t'-Hubbard model are discussed within a functional renormalization group
approach. The fermionic four-point vertex is efficiently parametrized by means
of partial bosonization. The exchange of composite bosons in the magnetic,
charge density and superconducting channels accounts for the increase of the
effective couplings with increasing length scale. We compute the pseudocritical
temperature for the onset of local order in various channels.Comment: 11 pages, 14 figures, equivalent to published versio
The phases with spontaneously broken symmetries corresponding to antiferromagnetic and d-wave superconducting order in the two-dimensional t − t -Hubbard model are investigated by means of the functional renormalization group. The introduction of composite boson fields in the magnetic, charge density, and superconducting channels allows an efficient parametrization of the four-fermion vertex and the study of regimes where either the antiferromagnetic or superconducting order parameter, or both, are nonzero. We compute the phase diagram and the temperature dependence of the order parameter below the critical temperature, where antiferromagnetic and superconducting order show a tendency of mutual exclusion.
Abstract:The paper proposes a novel approach to the much discussed question of which symmetries have direct empirical significance and which do not. The approach is based on a development of a recently proposed framework by Hilary Greaves and David Wallace, who claim that, contrary to the standard folklore among philosophers of physics, local symmetries may have direct empirical significance no less than global ones. Partly vindicating the standard folklore, a result is derived here from a number of quite plausible assumptions, which states that local symmetries can indeed have no direct empirical significance. Ways to interpret the result are considered and possible morals are outlined.
We investigate how the different velocities characterizing the low-energy
spectral properties and the low-temperature thermodynamics of one-dimensional
correlated electron systems (Luttinger liquids) affect the transport properties
of ring-like conductors. The Luttinger liquid ring is coupled to two
noninteracting leads and pierced by a magnetic flux. We study the flux
dependence of the linear conductance. It shows a dip structure which is
governed by the interaction dependent velocities. Our work extends an earlier
study which was restricted to rather specific choices of the interaction
parameters. We show that for generic repulsive two-particle interactions the
number of dips can be estimated from the ratio of the charge current velocity
and the spin velocity. In addition, we clarify the range of validity of the
central approximation underlying the earlier study.Comment: 10 pages including figure
The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of Elitzur's theorem. Nevertheless, gauge symmetry breaking does occur in gauge quantum field theories in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.
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