ترغب بنشر مسار تعليمي؟ اضغط هنا

Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction

124   0   0.0 ( 0 )
 نشر من قبل Volker Meden
 تاريخ النشر 2012
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical form are investigated all leading to universal Luttinger liquid physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the Luttinger liquid phenomenology. For generic regular potentials the large time decay of the momentum distribution function towards the steady-state value is characterized by a power law with a universal exponent which only depends on the potential at zero momentum transfer. A commonly employed ad hoc procedure fails to give this exponent. Besides quenches from zero to positive interactions we also consider abrupt changes of the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and the one obtained in equilibrium at equal two-particle interaction.



قيم البحث

اقرأ أيضاً

We investigate charge fractionalizations in artificial Tomonaga-Luttinger liquids (TLLs) composed of two capacitively coupled quantum Hall edge channels (ECs) in graphene. The interaction strength of the artificial TLLs can be controlled through dist ance W between the ECs. We show that the fractionalization ratio r and the TLL mode velocity v vary with W. The experimentally obtained relation between v and r follows a unique function predicted by the TLL theory. We also show that charged wavepackets are reflected back and forth multiple times at both ends of the TLL region.
395 - L. Markhof , V. Meden 2015
We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum-dependence of the two-particle interaction V(q). Usually, V(q) is assumed to be a constant a nd integrals are regularized in the ultraviolet `by hand employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense this does not affect the universal low-energy properties of the model, e.g. exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum k_F, with |k-k_F| setting a nonvanishing energy scale, the details of V(q) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum resolved spectral function as a function of energy. Even for |k-k_F| much smaller than the momentum space range of the interaction the spectral line shape depends on the details of V(q). The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi one-dimensional metals, and for recent attempts to compute the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account (nonlinear Luttinger liquid phenomenology) is discussed.
We demonstrate that quantum-critical spin dynamics can be probed in high magnetic fields using muon-spin relaxation ($mu^{+}$SR). Our model system is the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). In the gapless Tom onaga-Luttinger liquid phase we observe finite-temperature scaling of the $mu^{+}$SR $1/T_1$ relaxation rate which allows us to determine the Luttinger parameter $K$. We discuss the benefits and limitations of local probes compared with inelastic neutron scattering.
We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the chemical doping. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems, and trace back its physical origin to the anisotropic self-energies in the momentum space.
For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite size c orrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا