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arXiv:1905.05398 · Physical review. B./Physical review. B

Formation of localized magnetic states in a large-spin Fermi system

Bin‐Zhou Mi, Qiang Gu

Published May 9, 2019• 5 citations
arXivHTMLPDF

Abstract

We extend the Anderson impurity model to a large-spin Fermi system with spin $f=\frac{3}{2}$, stimulated by the realization of large-spin ultracold Fermi atoms. The condition required for the spontaneous formation of local magnetic moments is examined and the ground-state mean-field magnetic phase diagram is explored carefully. We find that the spin-$\frac{3}{2}$ Fermi system involves magnetic phase regions I, II, and III that correspond to one, two, and three particle/hole occupation, respectively. In addition, it is observed that all the three magnetic phases have fourfold-degenerate ground states. Finally, the phase transition between the three phases seems to be of the first order.

DOI
10.1103/physrevb.99.184405

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We extend the Anderson impurity model to a large-spin Fermi system with spin f=32f=\frac{3}{2}f=23​, stimulated by the realization of large-spin ultracold Fermi atoms. The condition required for the spontaneous formation of local magnetic moments is examined and the ground-state mean-field magnetic phase diagram is explored carefully. We find that the spin-32\frac{3}{2}23​ Fermi system involves magnetic phase regions I, II, and III that correspond to one, two, and three particle/hole occupation, respectively. In addition, it is observed that all the three magnetic phases have fourfold-degenerate ground states. Finally, the phase transition between the three phases seems to be of the first order.
The ultracold atomic Fermi gas provides a flexible and controllable experimental platform for exploring magnetic impurity states. In this study, we theoretically examine the magnetic impurity states in a Fermi system with spin-1/2 and spin-3/2 under a local magnetic field. Firstly, the spin-1/2 impurity system contains three types of magnetic solutions. One type magnetic solution with higher energy can be regarded as the result of induced magnetization of a trivial solution, while the other two types magnetic solutions with lower energy can be understood as the results of Zeeman splitting of nontrivial solutions with double degeneracy. Notably, the magnetic solution corresponding to the spin state parallel to the Zeeman magnetic field is always the most stable in terms of the energy. Secondly, we extend the idea of studying spin-1/2 impurity to spin-3/2 impurity, where the half-filled state of impurity atoms is calculated. We found that four types of magnetic solutions at zero magnetic field were split into four, six, four, and twelve new magnetic solutions in the presence of a Zeeman magnetic field, respectively. We obtained that the magnetic solution corresponding to the spin state parallel to the magnetic field is the most stable, and its energy is lower than that of the corresponding magnetic solution at zero magnetic field. Therefore, the introduction of a local magnetic field is beneficial for the formation of magnetic impurity states. Finally, the calculated data illustrate that the Anderson impurity model we adopt exhibits invariance under the combined transformations of spin-flip and particle-hole.
We study correlated quantum impurity models that undergo a local quantum phase transition (QPT) from a strong coupling, Fermi liquid phase to a non-Fermi liquid phase with a globally doubly degenerate ground state. Our aim is to establish what can be shown exactly about such ``local moment'' (LM) phases, of which the permanent (zero-field) local magnetization is a hallmark, and an order parameter for the QPT. A description of the zero-field LM phase is shown to require two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the single self-energy of standard field theory. Distinct Friedel sum rules for each phase are obtained, via a Luttinger theorem embodied in the vanishing of appropriate Luttinger integrals. By contrast, the standard Luttinger integral is nonzero in the LM phase but found to have universal magnitude. A range of spin susceptibilites are also considered, including that corresponding to the local order parameter, whose exact form is shown to be RPA-like, and to diverge as the QPT is approached. Particular attention is given to the pseudogap Anderson model, including the basic physical picture of the transition, the low-energy behavior of single-particle dynamics, the quantum critical point itself, and the rather subtle effect of an applied local field. A two-level impurity model that undergoes a QPT (``singlet-triplet'') to an underscreened LM phase is also considered, for which we derive on general grounds some key results for the zero-bias conductance in both phases.
Abstract. We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D ≥ 2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle-hole symmetric point the color superfluid phase is always spontaneously magnetized, leading to the formation of different color superfluid domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency to phase-separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) color superfluid also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.ar X iv
We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D ⩾2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle–hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.
We theoretically investigate two-particle and ground-state many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasiperiodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the ground-state many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional sss-wave interactions. As the disorder strength increases, the two-particle binding energy increases and the fermionic superfluidity of many particles disappears above a threshold. At a large Zeeman field, where the interatomic interaction behaves effectively like a ppp-wave interaction, the binding energy decreases with increasing disorder strength, and the resulting topological superfluidity shows a much more robust stability against disorder than the conventional sss-wave superfluidity. We also analyze the localization properties of the emergent Majorana fermions in the topological phase. Our results could be experimentally examined in future cold-atom experiments, where the spin-orbit coupling can be induced artificially by using two Raman lasers, and the quasiperiodic potential can be created by using bichromatic optical lattices.
A gas of ultracold 6{}^{6}6Li atoms (effective spin 1/2) confined to an elongated trap with one-dimensional properties is a candidate to display three different phases: (i) fermions bound in Cooper-pair-like states, (ii) unbound spin-polarized particles, and (iii) a mixed phase in which Cooper bound states and unpaired particles coexist. It is of great interest to extend these studies to fermionic atoms with higher spin, e.g., for neutral 40{}^{40}40K, 43{}^{43}43Ca, 87{}^{87}87Sr, or 173{}^{173}173Yb atoms. Within the grand-canonical ensemble, we investigated the $\ensuremath{\mu}$ versus HHH phase diagram ($\ensuremath{\mu}$ is the chemical potential and HHH the external magnetic field) for S=3/2,...,9/2S=3/2,...,9/2S=3/2,...,9/2 for the ground state using the exact Bethe ansatz solution of the one-dimensional Fermi gas with an attractive $\ensuremath{\delta}$-function interaction potential. There are N=2S+1N=2S+1N=2S+1 fundamental states: the particles can be either unpaired or clustered in bound states of 2, 3, $\ensuremath{\cdots}$, 2S2S2S, and 2S+12S+12S+1 fermions. The rich phase diagram consists of these NNN states and various mixed phases in which combinations of the fundamental states coexist. Bound states of NNN fermions are not favorable in high magnetic fields, but always present if the field is low. For S=3/2,S=3/2,S=3/2, possible scenarios for phase separation are explored within the local density approximation. For S=3/2,S=3/2,S=3/2, the phase diagram for the superposition of a Zeeman and a quadrupolar splitting is also discussed.