arXiv subjects

M. Pepe

Publications and source records attributed to M. Pepe.

At least 37 records · Page 2Linked to original sources

arXiv2007

Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

We have constructed a systematic low-energy effective theory for hole- and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at $(\pm\fracπ{2a},\pm\fracπ{2a})$ and where electrons live in pockets centered at $(\fracπ{a},0)$ or $(0,\fracπ{a})$. The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schrödinger equation. As a result, we find bound state wave functions that resemble $d_{x^2-y^2}$-like or $d_{xy}$-like symmetry. We also study possible ground states of lightly doped antiferromagnets.

cond-mat.str-el↗

arXiv2006

Systematic Low-Energy Effective Field Theory for Electron-Doped Antiferromagnets

In contrast to hole-doped systems which have hole pockets centered at $(\pm \fracπ{2a},\pm \fracπ{2a})$, in lightly electron-doped antiferromagnets the charged quasiparticles reside in momentum space pockets centered at $(\fracπ{a},0)$ or $(0,\fracπ{a})$. This has important consequences for the corresponding low-energy effective field theory of magnons and electrons which is constructed in this paper. In particular, in contrast to the hole-doped case, the magnon-mediated forces between two electrons depend on the total momentum $\vec P$ of the pair. For $\vec P = 0$ the one-magnon exchange potential between two electrons at distance $r$ is proportional to $1/r^4$, while in the hole case it has a $1/r^2$ dependence. The effective theory predicts that spiral phases are absent in electron-doped antiferromagnets.

cond-mat.str-el↗

arXiv2006

Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

The order parameter of a finite system with a spontaneously broken continuous global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with a spontaneously broken $SU(2)_s$ spin symmetry and massless QCD with a broken $SU(2)_L \times SU(2)_R$ chiral symmetry have rotor spectra when considered in a finite volume. When an electron or hole is doped into an antiferromagnet or when a nucleon is propagating through the QCD vacuum, a Berry phase arises from a monopole field and the angular momentum of the rotor is quantized in half-integer units.

cond-mat.other↗

arXiv2006

Exceptional Deconfinement in G(2) Gauge Theory

The Z(N) center symmetry plays an important role in the deconfinement phase transition of SU(N) Yang-Mills theory at finite temperature. The exceptional group G(2) is the smallest simply connected gauge group with a trivial center. Hence, there is no symmetry reason why the low- and high-temperature regimes in G(2) Yang-Mills theory should be separated by a phase transition. Still, we present numerical evidence for the presence of a first order deconfinement phase transition at finite temperature. Via the Higgs mechanism, G(2) breaks to its SU(3) subgroup when a scalar field in the fundamental {7} representation acquires a vacuum expectation value v. Varying v we investigate how the G(2) deconfinement transition is related to the one in SU(3) Yang-Mills theory. Interestingly, the two transitions seem to be disconnected. We also discuss a potential dynamical mechanism that may explain this behavior.

hep-lat↗

arXiv2006

Homogeneous versus Spiral Phases of Hole-doped Antiferromagnets: A Systematic Effective Field Theory Investigation

Using the low-energy effective field theory for magnons and holes -- the condensed matter analog of baryon chiral perturbation theory for pions and nucleons in QCD -- we study different phases of doped antiferromagnets. We systematically investigate configurations of the staggered magnetization that provide a constant background field for doped holes. The most general configuration of this type is either constant itself or it represents a spiral in the staggered magnetization. Depending on the values of the low-energy parameters, a homogeneous phase, a spiral phase, or an inhomogeneous phase is energetically favored. The reduction of the staggered magnetization upon doping is also investigated.

cond-mat.str-el↗

arXiv2006

Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schrödinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d_{x^2-y^2}-like symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.

cond-mat.str-el↗

arXiv2006

From the Hubbard Model to a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

The low-energy physics of antiferromagnets is governed by their Goldstone bosons -- the magnons -- and it is described by a low-energy effective field theory. In analogy to baryon chiral perturbation theory, we construct the effective field theory for magnons and holes in an antiferromagnet. It is a systematic low-energy expansion based on symmetry considerations and on the fact that the holes are located in pockets centered at k=(pi/2a,\pm pi/2a). Even though the symmetries are extracted from the Hubbard model, the effective theory is universal and makes model-independent predictions about the dynamical mechanisms in the antiferromagnetic phase. The low-energy effective theory has been used to investigate one-magnon exchange which leads to a d-wave-shaped bound state of holes.

cond-mat.str-el↗

arXiv2006

Efficient Cluster Algorithm for CP(N-1) Models

Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard Wilson formulation of lattice field theory. In fact, there is a no-go theorem that prevents the construction of an efficient Wolff-type embedding algorithm. In this paper, we construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a regularization for CP(N-1) models in the framework of D-theory. We present detailed studies of the autocorrelations and find a dynamical critical exponent that is consistent with z = 0.

hep-lat↗

arXiv2006

Magnon-mediated Binding between Holes in an Antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2ϕ)/r^2 where r is the distance vector of the holes and ϕis the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry. The role of these bound states as potential candidates for the preformed Cooper pairs of high-temperature superconductivity is discussed qualitatively.

cond-mat.str-el↗

arXiv2005

An Efficient Cluster Algorithm for CP(N-1) Models

We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a new regularization for CP(N-1) models in the framework of D-theory, which is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantum variables instead of classical fields. Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard formulation of lattice field theory. In fact, there is even a no-go theorem that prevents the construction of an efficient Wolff-type embedding algorithm. We present various simulations for different correlation lengths, couplings and lattice sizes. We have simulated correlation lengths up to 250 lattice spacings on lattices as large as 640x640 and we detect no evidence for critical slowing down.

hep-lat↗

arXiv2005

Simulating the High Energy Gamma-ray sky seen by the GLAST Large Area Telescope

This paper presents the simulation of the GLAST high energy gamma-ray telescope. The simulation package, written in C++, is based on the Geant4 toolkit, and it is integrated into a general framework used to process events. A detailed simulation of the electronic signals inside Silicon detectors has been provided and it is used for the particle tracking, which is handled by a dedicated software. A unique repository for the geometrical description of the detector has been realized using the XML language and a C++ library to access this information has been designed and implemented. A new event display based on the HepRep protocol was implemented. The full simulation was used to simulate a full week of GLAST high energy gamma-ray observations. This paper outlines the contribution developed by the Italian GLAST software group.

astro-ph↗

arXiv2004

Study of the 2-d CP(N-1) models at θ=0 and π

We present numerical results for 2-d CP(N-1) models at θ=0 and πobtained in the D-theory formulation. In this formulation we construct an efficient cluster algorithm and we show numerical evidence for a first order transition for CP(N-1\geq 2) models at θ= π. By a finite size scaling analysis, we also discuss the equivalence in the continuum limit of the D-theory formulation of the 2-d CP(N-1) models and the usual lattice definition.

hep-lat↗

arXiv2004

Deconfinement in Yang-Mills: a conjecture for a general gauge Lie group G

Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional scalar model symmetric under the center C(G) of G. These arguments have been investigated numerically only considering Yang-Mills theory with gauge symmetry in the G=SU(N) branch, where C(G)=Z(N). The symplectic groups Sp(N) provide another extension of SU(2)=Sp(1) to general N and they all have the same center Z(2). Hence, in contrast to the SU(N) case, Sp(N) Yang-Mills theory allows to study the relevance of the group size on the order of the deconfinement phase transition keeping the available universality class fixed. Using lattice simulations, we present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories both in (2+1)d and (3+1)d. We then make a conjecture on the order of the deconfinement phase transition in Yang-Mills theories with general Lie groups SU(N), SO(N), Sp(N) and with exceptional groups G(2), F(4), E(6), E(7), E(8). Numerical results for G(2) Yang-Mills theory at finite temperature in (3+1)d are also presented.

hep-lat↗

arXiv2004

Study of CP(N-1) θ-Vacua by Cluster-Simulation of SU(N) Quantum Spin Ladders

D-theory provides an alternative lattice regularization of the (1+1)-d CP(N-1) quantum field theory. In this formulation the continuous classical CP(N-1) fields emerge from the dimensional reduction of discrete SU(N) quantum spins. In analogy to Haldane's conjecture, ladders consisting of an even number of transversely coupled spin chains lead to a CP(N-1) model with vacuum angle θ= 0, while an odd number of chains yields θ= π. In contrast to Wilson's formulation of lattice field theory, in D-theory no sign problem arises at θ= π, and an efficient cluster algorithm is used to investigate the θ-vacuum effects. At θ= πthere is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.

hep-lat↗

arXiv2004

Static quark potential and effective string corrections in the (2+1)-d SU(2) Yang-Mills theory

We report on a very accurate measurement of the static quark potential in SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d Z(2) and SU(3) pure gauge theories.

hep-lat↗

arXiv2004

Nonlinear Realization of Chiral Symmetry on the Lattice

We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.

hep-lat↗

arXiv2003

The Deconfinement Phase Transition of Sp(2) and Sp(3) Yang-Mills Theories in 2+1 and 3+1 Dimensions

Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional spin model symmetric under the center of G. For d=3 these arguments have been confirmed numerically only in the SU(2) case with center Z(2), simply because all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(1) to general N. Using lattice simulations, we find that the deconfinement phase transition of Sp(2) Yang-Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky-Yaffe conjecture, for (2+1)-d Sp(2) Yang-Mills theory we find the universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory the transition is first order both in 2+1 and in 3+1 dimensions. This suggests that the size of the gauge group -- and not the center symmetry -- determines the order of the deconfinement phase transition.

hep-lat↗

arXiv2003

String effects in SU(2) lattice gauge theory

We discuss the effective string picture for the confining regime of lattice gauge theories at zero and finite temperature. We present results of extensive Monte Carlo simulations - performed with the Luscher and Weisz algorithm - for SU(2) Yang-Mills theory in 2+1 dimensions. We also address the issue of "string universality" by comparing our results with those obtained in other lattice gauge theories.

hep-lat↗