arXiv subjects

M. E. Carrington

Publications and source records attributed to M. E. Carrington.

At least 19 recordsLinked to original sources

arXiv2026

The gauge invariance of non-perturbative vertex prescriptions

We study the gauge invariance of different continuum methods to include non-perturbative effects in gauge theories. We work with three dimensional quantum electrodynamics and implement vertices using two different methods: a set of coupled Schwinger-Dyson (SD) integral equations, and the self-consistent equations obtained from the 3-particle irreducible (3PI) effective action. We work in Landau gauge and assess the extent to which results are gauge invariant by checking how well the Ward identity is satisfied. Our results show that there is a fairly significant violation of the Ward identity at large coupling, although the 3PI effective theory is slightly better than the SD vertex. We also compare the results of both calculations with the commonly used Ball-Chiu ansatz and show that the agreement of the ansatz with both non-perturbative vertices is fairly good at small coupling but deviates more significantly at large coupling. We compare results for the two point functions of the theory and discuss the possible implications for phase transitions.

hep-th↗

arXiv2023

Effects of different 3D QED vertex ansaetze on critical coupling

We study the semi-metal/insulator phase transition in graphene using a Schwinger-Dyson approach. We consider various forms of vertex ansaetze to truncate the hierarchy of Schwinger-Dyson equations. We define a Ball-Chiu type vertex that truncates the equations without violating gauge invariance. We show that there is a family of these vertices, parametrized by a continuous parameter that we call a, all of which satisfy the Ward identity. We have calculated the critical coupling of the phase transition using different values of a. We have also tested a common approximation in which only the first term in the Ball-Chiu ansatz is included. This vertex is independent of a, and, although it is not gauge invariant, it has been used many times in the literature because of the numerical simplifications it provides. We have found that, with a one-loop photon polarization tensor, the results obtained for the critical coupling from the truncated vertex and the full vertex with a = 1 agree very well, but other values of a give significantly different results. We have also done a fully self-consistent calculation, in which the photons are backcoupled to the fermion degrees of freedom, for one choice a = 1. Our results show that when photon dynamics are correctly taken into account, it is no longer true that the truncated vertex and the full Ball-Chiu vertex with a = 1 agree well. The conclusion is that traditional vertex truncations do not really make sense in a system that does not respect Lorentz invariance, like graphene, and the need to include vertex contributions self-consistently is likely inescapable.

cond-mat.mes-hall↗

arXiv2022

Phase transitions in anisotropic graphene

We study the effect of anisotropy on phase transitions in graphene. We work with an low energy effective field theory which is strongly coupled, and solve a coupled set of Schwinger-Dyson equations. We show that the effect of anisotropy is to reduce the critical coupling.

cond-mat.mes-hall↗

arXiv2021

The effect of anisotropy on phase transitions in graphene

We study the effect of anisotropy (strain) on dynamical gap generation in graphene. We work with a low energy effective theory obtained from a tight-binding Hamiltonian expanded around the Dirac points in momentum space. We use a non-perturbative Schwinger-Dyson approach and calculate a coupled set of five momentum dependent dressing functions. Our results show that the critical coupling depends only weakly on the anisotropy parameter, and increases with greater anisotropy.

cond-mat.mes-hall↗

arXiv2019

Renormalization of the 4PI effective action using the functional renormalization group

Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equations that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest ($n$=2) level. In this paper we show how to obtain renormalized results from an $n$-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms.

hep-th↗

arXiv2019

Four loop scalar $ϕ^4$ theory using the functional renormalization group

We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.

hep-th↗

arXiv2019

The effect of a Chern-Simons term on dynamical gap generation in graphene

We study the effect of a Chern-Simons term on dynamical gap generation in a low energy effective theory that describes some features of mono-layer suspended graphene. We use a non-perturbative Schwinger-Dyson approach. We solve a set of coupled integral equations for eight independent dressing functions that describe fermion and photon degrees of freedom. We find a strong suppression of the gap, and corresponding increase in the critical coupling, as a function of increasing Chern-Simons coefficient.

cond-mat.other↗

arXiv2018

The role of frequency dependence in dynamical gap generation in graphene

We study the frequency dependencies of the fermion and photon dressing functions in dynamical gap generation in graphene. We use a low energy effective QED-like description, but within this approximation, we include all frequency dependent effects including retardation. We obtain the critical coupling by calculating the gap using a non-perturbative Dyson-Schwinger approach. Compared to the results of our previous calculation [1] which used a Lindhard screening approximation instead of including a self-consistently calculated dynamical screening function, the critical coupling is substantially reduced.

cond-mat.mes-hall↗

arXiv2017

The 2PI effective theory at next-to-leading order using the functional renormalization group

We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which can not be done using any known method by introducing counterterms.

hep-th↗

arXiv2017

Momentum broadening in unstable quark-gluon plasma

Quark-gluon plasma produced at the early stage of ultrarelativistic heavy ion collisions is unstable, if weakly coupled, due to the anisotropy of its momentum distribution. Chromomagnetic fields are spontaneously generated and can reach magnitudes much exceeding typical values of the fields in equilibrated plasma. We consider a high energy test parton traversing an unstable plasma that is populated with strong fields. We study the momentum broadening parameter $\hat q$ which determines the radiative energy loss of the test parton. We develop a formalism which gives $\hat q$ as the solution of an initial value problem, and we focus on extremely oblate plasmas which are physically relevant for relativistic heavy ion collisions. The parameter $\hat q$ is found to be strongly dependent on time. For short times it is of the order of the equilibrium value, but at later times $\hat q$ grows exponentially due to the interaction of the test parton with unstable modes and becomes much bigger than the value in equilibrium. The momentum broadening is also strongly directionally dependent and is largest when the test parton velocity is transverse to the beam axis. Consequences of our findings for the phenomenology of jet quenching in relativistic heavy ion collisions are briefly discussed.

hep-ph↗

arXiv2016

Gradient Flow in the Ginzburg-Landau Model of Superconductivity

We present numerical studies of the dynamics of vortices in the Ginzburg Landau model using equations derived from the gradient flow of the free energy. These equations have previously been proposed to describe the dynamics of n-vortices away from equilibrium. We are able to model the dynamics of multiple n-vortex configurations starting far from equilibrium. We find generically that there are two time scales for equilibration: a short time scale related to the formation time for a single n-vortex, and a longer time scale that characterizes vortex-vortex interactions.

hep-th↗

arXiv2016

Dynamical gap generation in graphene with frequency dependent renormalization effects

We study the frequency dependencies in the renormalization of the fermion Greens function for the $π$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.

cond-mat.mes-hall↗

arXiv2016

The 2PI effective action at four loop order in $φ^4$ theory

It is well known that perturbative pressure calculations show poor convergence. Calculations using a two particle irreducible (2PI) effective action show improved convergence at the 3 loop level, but no calculations have been done at 4 loops. We consider the 2PI effective theory for a symmetric scalar theory with quartic coupling in 4-dimensions. We calculate the pressure and two different non-perturbative vertices as functions of coupling and temperature. Our results show that the 4 loop contribution can become larger than the 3 loop term when the coupling is large. This indicates a breakdown of the 2PI approach, and the need for higher order $n$PI approximations. In addition, our results demonstrate the renormalizability of 2PI calculations at the 4 loop level. This is interesting because the counterterm structure of the 2PI theory at 4 loops is different from the structure at $n\le 3$ loops. Two vertex counterterms are required at the 4 loop level, but not at lower loop order. This unique feature of the 2PI theory has not previously been verified numerically.

hep-th↗

arXiv2015

On the geometric measure of entanglement for pure states

The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it simplifies the calculations and allows for analytic solutions. Although some symmetry is required in order to deal with large numbers of qubits, we are able to loosen significantly the restrictions on the highly symmetric states considered previously, and consider several generalizations of the coefficients of both target and unentangled states. This allows us to compute the geometric entanglement measure for larger and more relevant classes of states.

quant-ph↗

arXiv2014

Renormalization group methods and the 2PI effective action

We consider a symmetric scalar theory with quartic coupling in 4-dimensions and compare the standard 2PI calculation with a modified version which uses a functional renormalization group method. The set of integral differential equations that are obtained from the exact renormalization group method truncate naturally, without the introduction of additional approximations. The results of the two methods agree well, which shows that the exact renormalization group can be used at the level of the 2PI effective action to obtain finite results without the use of counter-terms. The method therefore offers a promising starting point to study the renormalization of higher order $n$PI theories.

hep-ph↗

arXiv2013

Renormalization group flow equations from the 4PI equations of motion

The 4PI effective action provides a a hierarchy of integral equations which have the form of Bethe-Salpeter equations. The vertex functions obtained from these equations can be used to truncate the exact renormalization group flow equations. This truncation has the property that the flow is a total derivative with respect to the flow parameter and is equivalent to solving the nPI equations of motion. This result establishes a direct connection between two non-perturbative methods.

hep-th↗

arXiv2013

4-point vertices from the 2PI and 4PI Effective Actions

We consider a symmetric scalar theory with quartic coupling in 2- and 3-dimensions and compare the self-consistent 4-point vertex obtained from the 4PI effective action with the Bethe-Salpeter 4-vertex from 2PI effective action. At zero external momenta the two vertices agree well with each other when the coupling strength is small, but differences between them become more and more pronounced as the coupling strength is increased. We also study the momentum dependence of the two vertices and show that for certain momentum configurations they are almost identical, but differ for general momentum arguments.

hep-ph↗

arXiv2013

Bethe-Salpeter Equations from the 4PI effective action

In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that, together with the equation of motion for the self-consistent 4-vertex, these integral equations are closed, and that their expansions give infinite series of connected diagrams which have the correct symmetry.

hep-ph↗