arXiv subjects

Federico L. Bottesi

Publications and source records attributed to Federico L. Bottesi.

9 recordsLinked to original sources

arXiv2025

Bosonic Bogoliubov transformations as Lorentz boosts in $(c,{\overline c})=(1,1)$ conformal field theories with marginal $J{\overline J }$ deformations

We consider conformal field theories with central charges $(c,{\overline c})=(1,1)$ that are invariant under the exchange of the holomorphic and antiholomorphic sectors, in both bosonic and fermionic realizations that are meaningful for condensed matter systems. The effect of marginal current-current $(J,{\overline J})$ perturbations is to induce a deformation of the Hilbert space given by a Lorentz boost in the 2D space of currents, which is identified with a Bogoliubov transformation. The rapidity of the boost is determined by the coupling constant of the marginal perturbation. When the perturbation is diagonal in the original currents of the theory, there is a linear relation between the two, and non-linear otherwise. In the fermionic cases, both free and with Calogero-Sutherland interactions, the marginal perturbation corresponds to backward scattering processes.

hep-th↗

arXiv2025

Quantum dynamics of the effective field theory of the Calogero-Sutherland model

We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W-infinity algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model.

hep-th↗

arXiv2025

Effective short distance interaction in Calogero-Sutherland quantum fluids

We consider the effective conformal field theory with symmetry W-infinity x W-infinity that describes the thermodynamic limit of the Calogero-Sutherland model. In the repulsive regime of the free fermion formulation, we identify an attractive interaction between opposite moving particle-hole pairs that dominates the short distance behavior and that is proposed as responsible for the destabilization of the ground state, leading to a new one of bosonic nature. The process is described by a Bogoliubov transformation of the free fermion bilinear operators into bosonic ones, preserving the form of the W-infinity algebra but decoupling the opposite chirality terms in the hamiltonian, as expected in the low energy limit. In coordinate space this interaction has a short range component that arises due to the quantum regularization of the theory. The described dynamical process may be considered as a mechanism of the emergence of the known charge and quantum statistics fractionalization of the low lying excitations of the theory, as predicted in both first and second quantization studies.

hep-th↗

arXiv2024

Laminar flow of charged quantum fluids of the Calogero-Sutherland universality class

The effective field theory of the Calogero-Sutherland model represents a universality class of quantum hydrodynamic fluids in one spatial dimension. It describes quantum compressible fluids involving both chiralities in which the chiral density field obeys the quantum Benjamin-Ono equation. An extension of this theory to describe a laminar flow of the Calogero-Sutherland fluids in a rectangular geometry with small transverse width and the topology of a ribbon, is considered here. The physical picture is based on the edge states in the hierarchical quantum Hall effect, which may be seen as a collection of parallel one-dimensional quantum incompressible fluids moving along but confined within the transverse microscopic width of the edge of the sample. The effective theory is thus defined as the direct product of two one-dimensional theories of the Calogero-Sutherland class so that one involves motion while the other is confining. Charge transport may be induced by coupling the system to an external electromagnetic field that yields a global translation of the ground state. The effective theory describes quantum solitonic excitations along the direction of the flow and possesses a two-dimensional electric current density which shows a Wigner semicircle law profile in the transverse direction, suggesting a Poiseuille-like behavior but without dissipative viscous effects since the velocity of the fluid is not a well-defined quantum field. This simple physical picture predicts interesting phenomena with distinctive signatures that may be tested in real samples.

hep-th↗

arXiv2019

Universal power-law exponents in differential tunneling conductance for planar insulators near Mott criticality at low temperatures

We consider the low-temperature differential tunneling conductance $G$ for interfaces between a planar insulating material in the Mott-class and a metal. For values of the the applied potential difference $V$ that are not very small, there is a experimentally observed universal regime in which $G \sim V^m$, where $m$ is a universal exponent. We consider the theoretical prediction of the values of $m$ by using the method of Effective Field Theory ($EFT$), which is appropriate for discussing universal phenomena. We describe the Mott material by the $EFT$ pertaining the long-distance behavior of a spinless Hubbard-like model with nearest neighbors interactions previously considered. At the Mott transition, the $EFT$ is known to be given by a double Abelian Chern-Simons theory. The simplest realization of this theory at the tunneling interface yields a Conformal Field Theory with central charges $(c,\bar c) =(1,1)$ and Jain filling fraction $ν= 2/3$ describing a pair of independent counter-propagating chiral bosons (one charged and one neutral). Tunneling from the material into the metal is, therefore, described by this $EFT$ at the Mott critical point. The resulting tunneling conductance behaves as $G \sim V^{(1/ν-1)}$, yielding the prediction $m=1/2$, which compares well (within a $10 \%$ deviation) with the results for this exponent in two experimental studies considered here.

cond-mat.str-el↗

arXiv2015

Critical Theory of Two-Dimensional Mott Transition: Integrability and Hilbert Space Mapping

We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).

cond-mat.str-el↗

arXiv2010

Effective Field Theory and Integrability in Two-Dimensional Mott Transition

We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a consequence of a recently found solution of the Zamolodchikov Tetrahedron Equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U_q(sl(2))xU_q(sl(2)), with deformation parameter q=-1. Based on this result, the low-energy Effective Field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k=1 (with the standard normalization). By further employing the Effective Filed Theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.

cond-mat.str-el↗

arXiv2008

Mott transition and integrable lattice models in two dimensions

We describe the two-dimensional Mott transition in a Hubbard-like model with nearest neighbors interactions based on a recent solution to the Zamolodchikov tetrahedron equation, which extends the notion of integrability to two-dimensional lattice systems. At the Mott transition, we find that the system is in a d-density wave or staggered flux phase that can be described by a double Chern Simons effective theory with symmetry \su2 \otimes \su2. The Mott transition is of topological nature, characterized by the emergence of vortices in antiferromagnetic arrays interacting strongly with the electric charges and an electric-magnetic duality. We also consider the effect of small doping on this theory and show that it leads to a quantum gas-liquid coexistence phase, which belongs to the Ising universality class and which is consistent with several experimental observations.

cond-mat.str-el↗

arXiv2008

Effective Field Theories for Electrons in Crystalline Structures

We present an effective field theory formulation for a class of condensed matter systems with crystalline structures for which some of the discrete symmetries of the underlying crystal survive the long distance limit, up to mesoscopic scales, and argue that this class includes interesting materials, such as $Si$-doped $GaAs$. The surviving symmetries determine a limited set of possible effective interactions, that we analyze in detail for the case of $Si$-doped $GaAs$ materials. These coincide with the ones proposed in the literature to describe the spin relaxation times for the $Si$-doped $Ga As$ materials, obtained here as a consequence of the choice of effective fields and their symmetries. The resulting low-energy effective theory is described in terms of three (six chiral) one-dimensional Luttinger liquid systems and their corresponding intervalley transitions. We also discuss the Mott transition within the context of the effective theory.

cond-mat.mes-hall↗