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Giuseppe Benfatto

Publications and source records attributed to Giuseppe Benfatto.

7 recordsLinked to original sources
arXiv2015

Kondo effect in a fermionic hierarchical model

In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2 impurity. This model is proved to be exactly solvable, and is shown to exhibit a Kondo effect, i.e. that, if the interaction between the impurity and the electrons is antiferromagnetic, then the magnetic susceptibility of the impurity is finite in the 0-temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently non-perturbative. This difficulty is overcome by using the exact solvability of the model, which follows both from its fermionic and hierarchical nature.

cond-mat.stat-mech↗
arXiv2013

Universality of one-dimensional Fermi systems, I. Response functions and critical exponents

The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each others by model-independent formulas. We establish such relations, the proof of which has represented a challenging mathematical problem, for a general model of spinning fermions on a one dimensional lattice; interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature. Proofs are reported in two papers: in the present one, we demonstrate that the zero temperature response functions in the thermodynamic limit are Borel summable and have anomalous power-law decay with multiplicative logarithmic corrections. Critical exponents are expressed in terms of convergent expansions and depend on all the model details. All results are valid for the special case of the Hubbard model.

math-ph↗
arXiv2013

Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure

We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to asymptotically emerging symmetries. This is done by introducing an effective model verifying extra symmetries and by relating its critical exponents to those of the fermion lattice gas by suitable fine tuning of the parameters.

math-ph↗
arXiv2011

Universal Luttinger Liquid Relations in the 1D Hubbard Model

We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verify the universal Luttinger liquid relations. Borel summability and (a weak form of) Spin-Charge separation is established.

math-ph↗
arXiv2010

Drude weight in non solvable quantum spin chains

For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation $v_s^2=D/κ$, where $κ$ is the susceptibility and $v_s$ is the Fermi velocity. This result is proved by rigorous Renormalization Group methods and is true for any weakly interacting system, regardless its integrablity. This paper, combined with a previous paper of the same authors, completes the proof of the Luttinger liquid conjecture for such systems.

cond-mat.stat-mech↗
arXiv2004

Ward identities and Chiral anomaly in the Luttinger liquid

Systems of interacting non relativistic fermions in $d=1$, as well as spin chains or interacting bidimensional Ising models, verify an hidden approximate Gauge invariance which can be used to derive suitable Ward identities. Despite the presence of corrections and anomalies, such Ward identities can be implemented in a Renormalization Group approach and used to exploit nontrivial cancellations which allow to control the flow of the running coupling constants; in particular this is achieved combining Ward identities, Dyson equations and suitable correction identities for the extra terms appearing in the Ward identities, due to the presence of cutoffs breaking the local gauge symmetry. The correlations can be computed and show a Luttinger liquid behavior characterized by non universal critical indices, so that the general Luttinger liquid construction for one dimensional systems is completed without any use of exact solutions. The ultraviolet cutoff can be removed and a Quantum Field Theory corresponding to the Thirring model is also constructed.

cond-mat.other↗