According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupl
Green’sandspectralfunctionsofthesmallFr¨ohlichpolaron
A.S.AlexandrovandC.Sricheewin
DepartmentofPhysics,LoughboroughUniversity,LoughboroughLE113TU,U.K.
…… 此处隐藏1871字 ……
theoryisalmostexactinthenonadiabaticregimefor
allvaluesofthecouplingconstant.However,thereisno
agreementintheadiabaticregion,wherethe rstorder
perturbationexpressionoverestimatesthepolaronmass
byafewordersofmagnitudeintheintermediatecoupling
regime8.Hereω0isthecharacteristicphononfrequency
andtisthenearest-neighbourhoppingintegralsothat
1thedimensionlesscouplingconstantisλ=Ep/(zt).Amuchlowere ectivemassoftheadiabaticsmallpolaronintheintermediatecouplingregimecomparedwiththatestimatedby rstorderperturbationtheoryisaresultofpoorconvergenceoftheperturbationexpansiontotheappearanceofthefamiliardouble-wellpotential23intheadiabaticlimit.Thetunnellingprobabilityisex-tremelysensitivetotheshapethispotential.Ithasalsobeenunderstood21therangeofappli-cabilityoftheanalyticaltheory3,4stronglydependsontheradiusofinteraction.Whiletheanalyticalapproachisapplicableonlyifω0≥tforshort-rangeinteraction,thetheoryappearsalmostexactinasubstantiallywiderregionoftheparametersforalong-range(Fr¨ohlich)in-teraction.Theexacte ectivemassofbothsmallandlargeFr¨ohlichpolarons,calculatedwiththecontinuous-timepath-integralQuantumMonteCarlo(QMC)algo-rithm,m (λ)iswell ttedbyasingleexponent,22.Asanexample,e0.73λforω0=tande1.4λforω0=0.5tdescribem (λ)inaone-dimensionallattice.Thenumer-icalexponentsareremarkablyclosetothoseobtainedfromtheLang-Firsovtransformation,e0.78λande1.56λ,respectively.Hence,inthecaseoftheFr¨ohlichinterac-tionthetransformationisperfectlyaccuratealreadyinthe rstorderof1/λexpansionevenintheadiabaticregime,ω0/t≤1foranycouplingstrength.Inthispaperweusethisresulttocalculatethesingle-particleGreen’sfunctionofafermiononalatticecoupledwiththebosonic eldviathelong-rangeFr¨ohlichinter-action.2.Green’sfunctionsofthesmallFr¨ohlichpolaronTheclassicalapproachtothesmallpolaronproblemisbasedonthecanonicaldisplacement(Lang-Firsov)trans-formationoftheelectron-phononHamiltonian3allowingforthesummationofalldiagramsincludingthevertexcorrections, ωqn i[ui(q)dq+H.c.]c+t(m n)δs,s′c H=ij+i,j qq,iωq(d qdq+1/2)(1)withthebarehoppingintegralt(m)andthematrixele-mentoftheelectron-phononinteractionui(q)=1γ(q)eiq·m.2N(2)Herei=(m,s),j=(n,s′),includesitemandspins,n i=c ici,andci,dqareelectron(hole)andphononoperators,respectively.