Lowest Matsubara Frequency Research Articles

Fingerprints of the Local Moment Formation and its Kondo Screening in the Generalized Susceptibilities of Many-Electron Problems.

We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.

Dual parquet scheme for the two-dimensional Hubbard model: Modeling low-energy physics of high- Tc cuprates with high momentum resolution

We present a method to treat the two-dimensional (2D) Hubbard model for parameter regimes which are relevant for the physics of the high-${T}_{c}$ superconducting cuprates. Unlike previous attempts to attack this problem, our approach takes into account all fluctuations in different channels on equal footing and is able to treat reasonable large lattice sizes up to $32\ifmmode\times\else\texttimes\fi{}32$. This is achieved by the following three-step procedure: (i) We transform the original problem to a representation (dual fermions) in which all purely local correlation effects from the dynamical mean field theory are already considered in the bare propagator and bare interaction of the new problem. (ii) The strong $1/{(i\ensuremath{\nu})}^{2}$ decay of the bare propagator allows us to integrate out all higher Matsubara frequencies aside from the lowest using low-order diagrams. The new effective action depends only on the two lowest Matsubara frequencies which allows us to (iii) apply the two-particle self-consistent parquet formalism, which takes into account the competition between different low-energy bosonic modes in an unbiased way, on much finer momentum grids than usual. In this way, we were able to map out the phase diagram of the 2D Hubbard model as a function of temperature and doping. Consistently with the experimental evidence for hole-doped cuprates and previous dynamical cluster approximation calculations, we find an antiferromagnetic region at low doping and a superconducting dome at higher doping. Our results also support the role of the van Hove singularity as an important ingredient for the high value of ${T}_{c}$ at optimal doping. At small doping, the destruction of antiferromagnetism is accompanied by an increase of charge fluctuations supporting the scenario of a phase-separated state driven by quantum critical fluctuations.

TOPOLOGICAL SUSCEPTIBILITY AT FINITE TEMPERATURE IN A RANDOM MATRIX MODEL

The temperature and quark mass dependence of the topological susceptibility is analyzed in a random matrix model. A model combining random matrices and the lowest Matsubara frequency is known to describe the chiral phase transition of QCD qualitatively, but at finite temperature it suppresses the topological susceptibility in the thermodynamic limit by the inverse of the volume. We propose a modified model in which the topological susceptibility at finite temperature behaves reasonably. The modified model reproduces the chiral condensate and the zero-temperature result for the topological susceptibility of the conventional model, and it leads to a topological susceptibility at finite temperature in qualitative agreement with lattice QCD results.

Universality near zero virtuality

In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we obtain an exact, analytic expression for the average spectral density. In the large- n limit, the spectral density can be obtained from the solution to a cubic equation. This spectral density is nonzero in the vicinity of eigenvalue zero only for temperatures below the critical temperature of this model. Our main result is the demonstration that the microscopic limit of the spectral density is independent of temperature (apart from a temperature dependent scale factor expressed in terms of the chiral condensate) up to the critical temperature. This is due to a number of remarkable cancellations. This result provides strong support for the conjecture that the microscopic spectral density is universal. In our derivation, we emphasize the symmetries of the partition function and show that this universal behavior is closely related to the existence of an invariant saddle-point manifold.