Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron-soliton systems--the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

BasedontheHolsteinmodelHamiltonianofone-dimensionalmolecularcrystals,bymakinguseoftheexpansionapproachofthecorrelatedsqueezed-coherentstatesofphononinsteadofthetwo-phononcoherentstateexpansionscheme,thepropertiesofthegroundstateandtheanomalousquantumfluctuationsareinvestigatedinastronglycoupledelectron-phononsystemwithspecialconsiderationoftheelectron-two-phononinteraction.Theeffectiverenormalization(αi)ofthedisplacementofthesqueezedphononswiththeeffectofthesqueezed-coherentstatesofphononandboththeelectron-displacedphononandthepolaron-squeezedphononcorrelationshavebeencombinedtoobtaintheanomalousquantumfluctuationsforthecorrectionsofthecoherentstate.Duetothesenon-adiabaticcorrelations,theeffectivedisplacementparameterαiislargerthantheordinaryparameterα(0)i.Incomparisonwiththeelectron-one-phononinteraction(g)correctedasαig,wehavefoundtheelectron-two-phononinteraction(g1)correctedasαi2g1isenhancedsignificantly.Forthisreason,thegroundstateenergy(E(2)0)contributedbytheelectron-two-phononinteractionismorenegativethanthesingle-phononcase(E(1)0)andthesolitonsolutionismorestable.Atthesametime,theeffectsoftheelectron-two-phononinteractiongreatlyincreasethepolaronenergyandthequantumfluctuations.Furthermore,inadeeperlevel,wehaveconsideredtheeffectofthepolaron-squeezedphononcorrelation(f-correlation).Sincethiscorrelationparameterf>1,thiseffectwillstrengthentheelectron-oneandtwo-phononinteractionsbyfαigandf2αi2g1,respectively.Thefinalresultsshowthatthegroundstateenergyandthepolaronenergywillappearmorenegativefurtherandthequantumfluctuationswillgainfurtherimprovement.