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arXiv:1901.06914 · Physical review. B./Physical review. B

η -pairing in correlated fermion models with spin-orbit coupling

Li Kai

Published Oct 28, 2020• 12 citations
arXivHTMLPDF

Abstract

The authors study the $\ensuremath{\eta}$-pairing phenomenon in correlated fermion models with spin-orbit coupling. Spin-orbit coupled systems are usually thought to possess no continuous symmetries, except the conventional U(1) particle-number symmetry. The $\ensuremath{\eta}$-pairing reveals an exact SU(2) pseudospin symmetry in a broad class of spin-orbit coupled Hubbard models. Furthermore, the authors construct an exactly solvable interacting Dirac-semimetal model that exhibits an exact pseudospin symmetry with fine-tuned parameters. This model hosts $\ensuremath{\eta}$-pairing and charge density wave ground states, which meet at an exactly solvable multicritical line.

DOI
10.1103/physrevb.102.165150

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The authors study the \ensuremathη\ensuremath{\eta}\ensuremathη-pairing phenomenon in correlated fermion models with spin-orbit coupling. Spin-orbit coupled systems are usually thought to possess no continuous symmetries, except the conventional U(1) particle-number symmetry. The \ensuremathη\ensuremath{\eta}\ensuremathη-pairing reveals an exact SU(2) pseudospin symmetry in a broad class of spin-orbit coupled Hubbard models. Furthermore, the authors construct an exactly solvable interacting Dirac-semimetal model that exhibits an exact pseudospin symmetry with fine-tuned parameters. This model hosts \ensuremathη\ensuremath{\eta}\ensuremathη-pairing and charge density wave ground states, which meet at an exactly solvable multicritical line.
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the $\ensuremath{\eta}$-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in one dimension (where $\ensuremath{\eta}$ states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.
The existence of $\ensuremath{\eta}$-pairing eigenstates in the fermionic Hubbard model is fundamentally rooted in the $\ensuremath{\eta}$-pairing symmetry, which may hold for systems with nonuniform Hubbard interaction UUU. In this work, we present a generalized Hubbard model containing a variety of pseudospin terms that break the SO4{\mathrm{SO}}_{4}SO4​ symmetry but retain the $\ensuremath{\eta}$-pairing symmetry. This allows us to construct a variety of correlated systems possessing $\ensuremath{\eta}$-pairing eigenstates. We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-$\ensuremath{\eta}$-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a method for the control of an $\ensuremath{\eta}$-pairing wave packet with the aid of a time-dependent Hamiltonian.
A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.
Synthetic spin-orbit coupling in cold atoms couples the pseudospin and spatial degrees of freedom, and therefore, the inherent spin symmetry of the system plays an important role. In systems of two pseudospin degrees, two particles contain symmetric states and antisymmetric states, but the spin symmetry can be mixed for more particles. This mixed spin symmetry has been overlooked and has not been investigated thoroughly. We study the role of mixed spin symmetry in the presence of spin-orbit coupling and consider a system of three bosons with two hyperfine states trapped in a harmonic potential. We investigate the ground state and the energy spectrum by implementing exact diagonalization. Similar to that in two-particle systems, the interplay between spin-orbit coupling and repulsive interactions between antialigned pseudospins increases the population of the unaligned spin components in the ground state. Also, the emergence of mixed-spin symmetric states compensates for the rise of the interaction energy. In contrast to two-particle systems, the pair correlation of the ground state is analogous to the Tonks-Girardeau gas even for relatively small contact interactions, and this feature is enhanced by the spin-orbit coupling.
Motivated by recent experiments on ultracold fermions we study the effect of the spin-orbit interaction in an exactly solvable one-dimensional model with strong local attractive correlations between the fermions. We show that the asymptotes of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by the spin-orbit coupling. In the mixed phase, the correlation functions consist of terms that are the product of a power law of the distance and an oscillating function of the distance. We obtain the critical exponents for superfluidity and density waves. The leading exponents decrease as a function of spin-orbit coupling. In particular, the exponent for superfluidity is the smallest one signaling an instability to a phase where a weak interchain coupling can produce superfluidity of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The spatial oscillation of the order parameter is also modified by the spin-orbit parameter, i.e., its modulation is not just given by the spin imbalance.
We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital, and $\ensuremath{\eta}$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models that include the Hund's rule coupling.