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Physica B Condensed Matter

Single-particle excitation spectrum of infinite-dimensional Hubbard model under finite magnetic field

Tetsuro Saso, Akira Oguri

Published Feb 1, 1995• 3 citations
Publisher
DOI
10.1016/0921-4526(94)00399-g

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In this chapter we want to refine the analysis of the ground state and low-lying excitations of the Hubbard model in the phases with gapless modes, i.e. phases II, IV and V discussed in Chapters 6, 7, by taking account of corrections which are important when considering Hubbard chains of finite length L . For the generic case, i.e. away from half-filling in a magnetic field, the finite-size corrections to the spectrum of the Hubbard model have been calculated by F. Woynarovich [487]. These results are the basis for our discussion in the following Chapter 9 of the asymptotic behaviour of correlation functions within the conformal approach [6, 51, 62, 75] and thereby will allow us to make contact with Haldane's Luttinger liquid approach for the description of one-dimensional strongly correlated electron systems [189–192] Generic case – the repulsive Hubbard model in a magnetic field To investigate how the thermodynamic limit is approached we have to take into account finite-size corrections in our previous derivation of integral equations from Takahashi's equations. This analysis has to be performed separately for each of the phases with gapless excitations identified before. From a technical point of view the most complex situation is found in phase IV – the partially filled, partially magnetized band with two massless modes. The finite-size scaling behaviour in the phases with a single gapless mode can be studied using the same techniques and we will point out the differences to the ‘generic’ case studied in this section later in this chapter.

Cambridge University Press eBooks•Feb 7, 2005•0 citations
We address the question how a correspondence between the particle like excitations in the one dimensional Hubbard model (i.e. “holons ” and “spinons”) and the free fermionic picture can be estabilished in the limit of vanishing interaction by studying the finite size spectrum in the framework of the Bethe Ansatz. Special attention has to be paid to the case of a vanishing magnetic field where the two bands of excitations in either description are degenerate. The interaction lifts this degeneracy.
In this chapter we want to refine the analysis of the ground state and low-lying excitations of the Hubbard model in the phases with gapless modes, i.e. phases II, IV and V discussed in Chapters 6, 7, by taking account of corrections which are important when considering Hubbard chains of finite length L . For the generic case, i.e. away from half-filling in a magnetic field, the finite-size corrections to the spectrum of the Hubbard model have been calculated by F. Woynarovich [487]. These results are the basis for our discussion in the following Chapter 9 of the asymptotic behaviour of correlation functions within the conformal approach [6, 51, 62, 75] and thereby will allow us to make contact with Haldane's Luttinger liquid approach for the description of one-dimensional strongly correlated electron systems [189–192] Generic case – the repulsive Hubbard model in a magnetic field To investigate how the thermodynamic limit is approached we have to take into account finite-size corrections in our previous derivation of integral equations from Takahashi's equations. This analysis has to be performed separately for each of the phases with gapless excitations identified before. From a technical point of view the most complex situation is found in phase IV – the partially filled, partially magnetized band with two massless modes. The finite-size scaling behaviour in the phases with a single gapless mode can be studied using the same techniques and we will point out the differences to the ‘generic’ case studied in this section later in this chapter.