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arXiv:cond-mat/9907164 · Journal of the Physical Society of Japan

Critical Properties in Dynamical Charge Correlation Function for the One-Dimensional Mott Insulator

Tatsuya Fujii, Norio Kawakami

Published Jul 15, 1999• 3 citations
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Abstract

Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find that the edge singularity in the charge correlation function is governed by massless spinon excitations, although it is naively expected that spinons do not directly contribute to the charge excitation over the Hubbard gap. We obtain the momentum-dependent anomalous critical exponent by applying the finite-size scaling analysis to the Bethe ansatz solution of the half-filled Hubbard model.

DOI
10.1143/jpsj.68.2331

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Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find that the edge singularity in the charge correlation function is governed by massless spinon excitations, although it is naively expected that spinons do not directly contribute to the charge excitation over the Hubbard gap. We obtain the momentum-dependent anomalous critical exponent by applying the finite-size scaling analysis to the Bethe ansatz solution of the half-filled Hubbard model.
The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.
On the basis of the Bethe ansatz solution, the characteristic properties of charge excitations are investigated for the one-dimensional Hubbard model by inserting a charged hole into the Mott insulator. The density of states for the charged hole shows divergent behavior in the lower-energy region, whose connection is discussed analytically with the compressibility and magnitude of the Hubbard gap. Momentum-dependent susceptibility is also investigated within the framework of the quasiparticle formalism in the Bethe ansatz method. The logarithmic anomaly of the susceptibilty for the charged hole near 4kF{k}_{F}kF​ (kF{k}_{F}kF​ being the Fermi momentum in the noninteracting case) is considerably enhanced in the vicinity of the Mott insulating phase, while it is suppressed at the insulating phase due to the formation of the Hubbard gap.
Abstract We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and the k − Λ string bound states at arbitrary driving fields, showing subtle differences in spin magnons and charge η -pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.
We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.
We analyse the thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the ‘spin-disordered regime’, which is characterized by the temperature being much larger than the magnetic energy scale, but small compared to the Mott–Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal–insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott–Hubbard transition in the limit of infinite dimensions.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/21/21/2 atom systems is discussed.