arXiv subjects

N. Magnoli

Publications and source records attributed to N. Magnoli.

At least 19 recordsLinked to original sources

arXiv2022

On the behaviour of the interquark potential in the vicinity of the deconfinement transition

In the vicinity of the deconfinement transition the behaviour of the interquark potential can be precisely predicted using the Effective String Theory (EST). If the transition is continuous we can combine EST results with a conformal perturbation analysis and reach the degree of precision needed to detect the corrections beyond the Nambu-Goto approximation in the EST. We discuss in detail this issue in the case of the deconfinement transition of the SU(2) gauge theory in $(2+1)$ dimensions (which belongs to the same universality class of the 2d Ising model) by means of an extensive set of high precision simulations. We show that the Polyakov loops correlator of the SU(2) model is precisely described by the spin-spin correlator of the 2d Ising model not only at the critical point, but also down to temperatures of the order of $0.8 T_c$. Thanks to the exact integrability of the Ising model we can extend the comparison in the whole range of Polyakov loop separations, even beyond the conformal perturbation regime. We use these results to quantify the first EST correction beyond Nambu-Goto and show that it is compatible with the bounds imposed by a bootstrap analysis of EST. This correction encodes important physical information and may shed light on the nature of the flux tube and of its EST description.

hep-lat↗

arXiv2018

Conformal perturbation description of deconfinement

Conformal perturbation theory is a powerful tool to describe the behavior of statistical-mechanics models and quantum field theories in the vicinity of a critical point. In the past few years, it has been extensively used to describe two-dimensional models and recently has also been extended to three-dimensional models. We show here that it can also be used to describe the behavior of four-dimensional lattice gauge theories in the vicinity of a critical point. As an example, we discuss the two-point correlator of Polyakov loops close to the thermal deconfinement transition of $SU(2)$ Yang-Mills theory. We show that the short-distance behavior of this correlation function (and, thus, of the interquark potential) is described very well by conformal perturbation theory. This method is expected to work with a similarly high accuracy for all critical points in the same universality class, including, in particular, the critical endpoint in the QCD phase diagram.

hep-lat↗

arXiv2015

Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the $<σ(\mathbf {r})σ(0)>$, $<σ(\mathbf {r})ε(0)>$ and $<ε(\mathbf {r})ε(0)>$ correlators from which we extract the values of $C^σ_{σε}=1.07(3)$ and $C^ε_{εε}=1.45(30)$. Our estimate for $C^σ_{σε}$ agrees with those recently obtained using conformal bootstrap methods, while $C^ε_{εε}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

hep-th↗

arXiv2012

Finite frequency noise for edge states at filling factor $ν=2/5$

We investigate the properties of the finite frequency noise in a quantum point contact geometry for the fractional quantum Hall state at filling factor $ν=2/5$. The results are obtained in the framework of the Wen's hierarchical model. We show that the peak structure of the colored noise allows to discriminate among different possible excitations involved in the tunneling. In particular, optimal values of voltage and temperature are found in order to enhance the visibility of the peak associated with the tunneling of a 2-agglomerate, namely an excitation with charge double of the fundamental one associated to the single quasiparticle.

cond-mat.str-el↗

arXiv2012

Quasiparticle agglomerates in Read-Rezayi and anti Read-Rezayi state

We calculate the dominant excitations for the $k$-level ($k\in\mathbb{N}$) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi ($\bar{\textrm{RR}}$), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor $ν=2+ν^*$ with $ν^*=k/(k+2)$ for RR and $ν^*=2/(k+2)$ for $\bar{\textrm{RR}}$. In the $k$-level RR states, based on $\mathbb{Z}_k$ parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge $e^*_k= e/(k + 2)$, with $e$ the electron charge, if $k=2,3$. For k=4 the single-qp and the 2-agglomerate, with charge $2e^*_k$, have the same scaling and both dominate, while for $k>4$ the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the $k$-level $\bar{\textrm{RR}}$ states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of $k$. We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the $ν=5/2$, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.

cond-mat.str-el↗

arXiv2012

Tunneling between helical edge states through extended contacts

We consider a quantum spin Hall system in a two-terminal setup, with an extended tunneling contact connecting upper and lower edges. We analyze the effects of this geometry on the backscattering current as a function of voltage, temperature, and strength of the electron interactions. We find that this configuration may be useful to confirm the helical nature of the edge states and to extract their propagation velocity. By comparing with the usual quantum point contact geometry, we observe that the power-law behaviors predicted for the backscattering current and the linear conductance are recovered for low enough energies, while different power-laws also emerge at higher energies.

cond-mat.mes-hall↗

arXiv2012

Environmental induced renormalization effects in quantum Hall edge states

We propose a general mechanism for renormalization of the tunneling exponents in edge states of the fractional quantum Hall effect. Mutual effects of the coupling with out-of-equilibrium 1/f noise and dissipation are considered both for the Laughlin sequence and for composite co- and counter-propagating edge states with Abelian or non-Abelian statistics. For states with counter-propagating modes we demonstrate the robustness of the proposed mechanism in the so called disorder-dominated phase. Prototypes of these states, such as ν=2/3 and ν=5/2, are discussed in detail and the rich phenomenology induced by the presence of a noisy environment is presented. The proposed mechanism justifies the strong renormalizations reported in many experimental observations carried out at low temperatures. We show how environmental effects could affect the relevance of the tunneling excitations, leading to important implications in particular for the ν=5/2 case.

cond-mat.str-el↗

arXiv2012

Spectral noise for edge states at filling factor $ν=5/2$

We present a detailed analysis of finite frequency noise for the $ν=5/2$ fractional quantum Hall state in a quantum point contact geometry. The results are obtained within the Pfaffian and anti-Pfaffian models. We show that the behaviour of the coloured noise allows unambigously to discriminate among tunneling excitations with different charges. Optimal values of the external bias are found in order to emphasize the visibility of the noise peak associated with the tunneling of a 2-agglomerate, namely an excitation with charge double of the fundamental one. These correspond to the regime in which the bias is larger than the neutral modes cut-off frequency. The dependence on the temperature is also investigated in order to discriminate between the considered models.

cond-mat.str-el↗

arXiv2012

Non-Abelian BF theory for 2+1 dimensional topological states of matter

We present a field theoretical analysis of the 2+1 dimensional BF model with boundary in the Abelian and the non-Abelian case based on the Symanzik's separability condition. In both cases on the edges we obtain Kač--Moody algebras with opposite chiralities reflecting the time reversal invariance of the theory. While the Abelian case presents an apparent arbitrariness in the value of the central charge, the physics on the boundary of the non-Abelian theory is completely determined by time reversal and gauge symmetry. The discussion of the non-Abelian BF model shows that time reversal symmetry on the boundary implies the existence of counter-propagating chiral currents.

cond-mat.mes-hall↗

arXiv2011

Anomalous charge tunneling in the fractional quantum Hall edge states at filling factor ν= 5/2

We explain effective charge anomalies recently observed for fractional quantum Hall edge states at $ν=5/2$ [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys.Rev. B. \textbf{81}, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly take into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic $1/f$ noise. We demonstrate that a peculiar agglomerate excitation with charge $e/2$, double of the expected $e/4$ charge, dominates the transport properties at low energies.

cond-mat.str-el↗

arXiv2010

Maxwell-Chern-Simons Theory With Boundary

The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The boundary is introduced according to Symanzik's basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge does not depend on the Maxwell term.

hep-th↗

arXiv2009

Integrable structures in LGTs near the deconfinement transition

In this contribution we review some recent results about the emergence of 2D integrable systems in 3D Lattice Gauge Theories near the deconfinement transition. We focus on some concrete examples involving the flux tube thickness, the ratio of k-string tensions and Polyakov loops correlators in various models.

hep-lat↗

arXiv2006

Study of the flux tube thickness in 3d LGT's by means of 2d spin models

We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the correlation function in the two-dimensional spin model with Z_2 global symmetry, (i.e. the 2d Ising model) in the high-temperature phase. Using the form factor approach we obtain an explicit expression for this function and from it we infer the behaviour of the flux density of the original (2+1)d LGT. Remarkably enough the result we obtain for the flux tube thickness agrees (a part from an overall normalization) with the effective string prediction for the same quantity.

hep-th↗

arXiv2006

Signatures of fractional Hall quasiparticles in moments of current through an antidot

The statistics of tunneling current in a fractional quantum Hall sample with an antidot is studied in the chiral Luttinger liquid picture of edge states. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers in both the thermal and the shot limit. In addition, we address effects on current moments of non-universal exponents in single-quasiparticle propagators. Positive correlations, result of propagators behaviour, are obtained in the shot noise limit of the Fano factor, and possible experimental consequences are outlined.

cond-mat.mes-hall↗

arXiv2005

Potts correlators and the static three-quark potential

We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high-temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte-Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2+1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high-temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a Δtype law at short distances and a Y type law at large distances.

hep-th↗

arXiv2004

On the magnetic perturbation of the Ising model on the sphere

In this letter we will extend the analysis given by Al. Zamolodchikov for the scaling Yang-Lee model on the sphere to the Ising model in a magnetic field. A numerical study of the partition function and of the vacuum expectation values (VEV) is done by using the truncated conformal space (TCS) approach. Our results strongly suggest that the partition function is an entire function of the coupling constant.

hep-th↗

arXiv2003

A new class of short distance universal amplitude ratios

We propose a new class of universal amplitude ratios which involve the first terms of the short distance expansion of the correlators of a statistical model in the vicinity of a critical point. We will describe the critical system with a conformal field theory (UV fixed point) perturbed by an appropriate relevant operator. In two dimensions the exact knowledge of the UV fixed point allows for accurate predictions of the ratios and in many nontrivial integrable perturbations they can even be evaluated exactly. In three dimensional O(N) scalar systems feasible extensions of some existing results should allow to obtain perturbative expansions for the ratios. By construction these universal ratios are a perfect tool to explore the short distance properties of the underlying quantum field theory even in regimes where the correlation length and one point functions are not accessible in experiments or simulations.

hep-th↗

arXiv2002

Composite Fermions with Spin at $ν=1/2$

The model of Composite Fermions for describing interacting electrons in two dimensions in the presence of a magnetic field is described. In this model, charged Fermions are combined with an even number of magnetic flux quanta in such a way that the external magnetic field is compensated on the average for half filling of Landau levels and the interaction is incorporated into an effective mass of the new composite particles. The fluctuations of the Chern-Simons gauge field, which describes formally the flux attachment, induce new interactions between the Composite Fermions. The effective interaction is investigated with particular emphasis on the role of the electron spin at filling factor $ν=1/2$. For a system with equal numbers of spin-up and spin-down electrons it is found that the dominant effective interaction is attractive in the spin-singlet channel. This can induce a ground state consisting of Cooper pairs of Composite Fermions that is separated from the excited states by a gap. The results are used to understand recent spin polarization measurements done in the region of the Fractional Quantum Hall Effect at different constant filling factors.

cond-mat.mes-hall↗