arXiv subjects

Matteo Bazzanella

Publications and source records attributed to Matteo Bazzanella.

4 recordsLinked to original sources

arXiv2014

Non-Linear Methods in Strongly Correlated Electron Systems

We analyze the structure of the group of (local) non-linear canonical transformations that exist in a system with n fermionic modes. To perform our study we develop an alternative framework to represent the generators of these canonical transformations; indeed we show how their definition, understanding and control is significantly improved using the Majorana fermion representation. These canonical transformations have the structure of a Lie group and we provide a representation for the elements of the Lie algebra that is very convenient both conceptually and practically (computationally): indeed our framework yields as side product an extremely effective tool to handle and work with SU(2n) Lie groups and algebras. Granting an enhanced control of the group of non-linear canonical transformation, our framework can be helpful in the study of strongly correlated electron systems, since it allows to easily identify fermionic degrees of freedom able to capture part of the correlations and thus may give a simpler representation of the Hamiltonian. Thanks to our analysis, also symmetry-based studies of the quantum Hamiltonians can be improved, since the simple representation of the generators of the canonical group permits to identify and understand otherwise hidden symmetries of difficult interpretation. The main aim of this work is to provide a comprehensive, general and scrupulous analysis of this framework, that we already applied in some circumstances. Therefore specific applications will not be presented in detail, since they can be found elsewhere, while only the formal and conceptual aspects will be developed thoroughly.

cond-mat.str-el↗

arXiv2014

Free fermion description of a paramagnetic Mott insulator

A scheme is presented that enables a description of a paramagnetic Mott insulator in terms of free fermions. The main idea is to view the physical fermions as a part of a multi-band system and to allow for a correlation between the physical fermions and the auxiliary ones. Technically this is implemented through a non-linear canonical transformation, which is conveniently formulated in terms of Majorana fermions. The transformed Hamiltonian is in the next stage approximated with a free fermion theory. The approximation step is variational and provides an upper bound on the ground state energy at zero or the Free energy at finite temperature.

cond-mat.str-el↗

arXiv2013

Ferromagnetism in the one-dimensional Kondo lattice: mean-field approach via Majorana fermion canonical transformation

Using a canonical transformation it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. We investigate the effectiveness of this three fermion representation by performing a zero temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions agree in many respects with the known numerical and analytical results. In particular, in the ferromagnetic region connected to the solution at zero electron density, we have a quantitative agreement on the value of the commensurability parameter discovered in recent DMRG (in one dimension) and DMFT (in infinite dimensions) simulations; furthermore we provide a theoretical justification for it, identifying a symmetry of the Hamiltonian. This ferromagnetic phase is stabilized by the emergence of a spin-selective Kondo insulator that is described quite conveniently by the three spinless fermions. We discovered also a different ferromagnetic phase at high filling and low couplings. This phase resembles the RKKY ferromagnetic phase existing at vanishing filling, but it incorporates much more of the Kondo effect, making it energetically more favorable than the typical spiral (spin ordered) mean field ground states. We believe that this second phase represents a prototype for the strange ferromagnetic tongue identified by numerical simulations inside the paramagnetic dome. At the end of the work we also provide a discussion of possible orders different from the ferromagnetic one. In particular at half-filling, where we obtain as ground state at high coupling the correct Kondo insulating state.

cond-mat.str-el↗

arXiv2013

Majorana fermion description of the Kondo lattice: Variational and Path integral approach

All models of interacting electrons and spins can be reformulated as theories of interacting Majorana fermions. We consider the Kondo lattice model that admits a symmetric representation in terms of Majorana fermions. In the first part of this work we study two variational states, which are natural in the Majorana formulation. At weak coupling a state in which three Majorana fermions tend to propagate together as bound objects is favored, while for strong coupling a better description is obtained by having deconfined Majorana fermions. This way of looking at the Kondo lattice offers an alternative phenomenological description of this model. In the second part of the paper we provide a detailed derivation of the discretized path integral formulation of any Majorana fermion theory. This general formulation will be useful as a starting point for further studies, such as Quantum Monte Carlo, perturbative expansions, and Renormalization Group analysis. As an example we use this path integral formalism to formulate a finite temperature variational calculation, which generalizes the ground state variational calculation of the first part. This calculation shows how the formation of three-body bound states of Majorana fermions can be handled in the path integral formalism.

cond-mat.str-el↗