The one-dimensional SU $(n)$ Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for $n>2$ . It is found that in the half-filled case, the umklapp processes couple the spin and charge degrees of freedom and generate a finite gap for arbitrary finite positive $U$ . This behavior is thus different from that at $1∕n$ filling, where there is one particle per site, in which case the dynamics of the two degrees of freedom can be separated and a critical ${U}_{\mathrm{c}}$ is needed for the Mott transition.The one-dimensional SU$(n)$ Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for $n>2$. It is found that in the half-filled case, the umklapp processes couple the spin and charge degrees of freedom and generate a finite gap for arbitrary finite positive $U$. This behavior is thus different from that at $1∕n$ filling, where there is one particle per site, in which case the dynamics of the two degrees of freedom can be separated and a critical ${U}_{\mathrm{c}}$ is needed for the Mott transition.

Physical Review BMay 16, 200521 citations

Spin-charge separation in the 1D Hubbard model

Mona Berciu, Sajeev John

APSMar 1, 20000 citations

Charge and Spin separation in the Hubbard model in one dimension

V. E. Korepin

APSMar 1, 20010 citations

One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields

J. M. P. Carmelo, Tilen Čadež, Pedro D Sacramento

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- $1/2$ atom systems is discussed.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-$1/2$ atom systems is discussed.

arXiv:2105.06721Physical review. B./Physical review. BMay 13, 20219 citations

Spin and charge response to magnetic frustration in strongly correlated itinerant electron systems

Yang Liu, Changfeng Chen

We investigate the effects of magnetic frustration on spin and charge dynamics in strongly correlated itinerant electron systems by using the exact diagonalization technique. A Hubbard model with adjustable degree of magnetic frustration is constructed. Static and dynamic spin and charge correlation functions show different dependence on the degree of magnetic frustration in the system. With increasing magnetic frustration, the spin and charge correlation function spectra become more sparse, indicating a decreased level of mixing of the spin and charge degrees of freedom or a partial spin-charge separation.We investigate the effects of magnetic frustration on spin and charge dynamics in strongly correlated itinerant electron systems by using the exact diagonalization technique. A Hubbard model with adjustable degree of magnetic frustration is constructed. Static and dynamic spin and charge correlation functions show different dependence on the degree of magnetic frustration in the system. With increasing magnetic frustration, the spin and charge correlation function spectra become more sparse, indicating a decreased level of mixing of the spin and charge degrees of freedom or a partial spin-charge separation.

Physical review. B, Condensed matterFeb 27, 20010 citations

Charge-Spin Separation and Pairing in a Generalized Hubbard Model

C. Kübert, Alejandro Muramatsu

NATO ASI series. Series B : PhysicsJan 1, 19950 citations

The one-dimensional SU

(n)

Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for

n>2

. It is found that in the half-filled case, the umklapp processes couple the spin and charge degrees of freedom and generate a finite gap for arbitrary finite positive

U

. This behavior is thus different from that at

1∕n

filling, where there is one particle per site, in which case the dynamics of the two degrees of freedom can be separated and a critical

{U}_{\mathrm{c}}

is needed for the Mott transition.

1/2

atom systems is discussed.