Magnetic ordering of itinerant fermionic systems is at the forefront of condensed matter physics dating back to Stoner's instability. Spin-orbit coupling (SOC) which couples two essential ingredients of an itinerant fermionic system, namely spin and orbital motion, opens up new horizons to this long-standing problem. Here we report that the itinerant ferromagnetism is absent in 3D Fermi gas with a Weyl SOC and various itinerant spin density waves emerge instead, which is deeply rooted in the unique symmetry and spin-momentum locking effect in spin-orbit coupled systems. What is more appealing is that, the strong SOC provides a new and efficient mechanism to realize itinerant spin density waves at extremely weak repulsion---a significant benefit for present ultra-cold atom experiment. These novel phenomena can be probed by Bragg spectroscopy, time of flight imaging and {\sl In-Situ } measurements in ultra-cold atom experiment.
Magnetic ordering of itinerant fermionic systems is at the forefront of condensed matter physics dating back to Stoner's instability. Spin-orbit coupling (SOC) which couples two essential ingredients of an itinerant fermionic system, namely spin and orbital motion, opens up new horizons to this long-standing problem. Here we report that the itinerant ferromagnetism is absent in 3D Fermi gas with a Weyl SOC and various itinerant spin density waves emerge instead, which is deeply rooted in the unique symmetry and spin-momentum locking effect in spin-orbit coupled systems. What is more appealing is that, the strong SOC provides a new and efficient mechanism to realize itinerant spin density waves at extremely weak repulsion---a significant benefit for present ultra-cold atom experiment. These novel phenomena can be probed by Bragg spectroscopy, time of flight imaging and {\sl In-Situ } measurements in ultra-cold atom experiment.
Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.
Cold Atom Magnetism Magnetic ordering arises from the strong interactions between atoms, with its origins deeply rooted in quantum mechanics. How the ordering comes about, however, has long been a topic of debate because most condensed-matter systems are limited by a somewhat fixed parameter space. Cold atom systems, by comparison, provide the ability to tune the magnitude and sign of the atom-atom interaction, as well as the density. Jo et al. (p. 1521 ; see the Perspective by Zwerger ) exploit this flexibility to use an ensemble of ultracold fermionic atoms as a “quantum simulator” to explore the possibility of magnetic ordering. As the repulsive interaction between atoms is increased, an instability occurs in the free two-component Fermi gas (or jellium), which results in a phase transition and the ferromagnetic ordering of the atoms.
We investigate the itinerant ferromagnetism in a dipolar Fermi atomic system with the anisotropic spin–orbit coupling (SOC), which is traditionally explored with isotropic contact interaction. We first study the ferromagnetism transition boundaries and the properties of the ground states through the density and spin-flip distribution in momentum space, and we find that both the anisotropy and the magnitude of the SOC play an important role in this process. We propose a helpful scheme and a quantum control method which can be applied to conquering the difficulties of previous experimental observation of itinerant ferromagnetism. Our further study reveals that exotic Fermi surfaces and an abnormal phase region can exist in this system by controlling the anisotropy of SOC, which can provide constructive suggestions for the research and the application of a dipolar Fermi gas. Furthermore, we also calculate the ferromagnetism transition temperature and novel distributions in momentum space at finite temperature beyond the ground states from the perspective of experiment.
The current efforts of studying many-body effects with spin-orbit coupling (SOC) using alkali-metal atoms are impeded by the heating effects due to spontaneous emission. Here, we show that even for SOCs too weak to cause any heating, dramatic many-body effects can emerge in a one-dimensional (1D) spin-21 Fermi gas provided the interaction is sufficiently repulsive. For weak repulsion, the effect of a weak SOC (with strength $\ensuremath{\Omega}$) is perturbative, inducing a weak spin spiral (with magnitude proportional to $\ensuremath{\Omega}$). However, as the repulsion g increases beyond a critical value (${g}_{c}\ensuremath{\sim}1/\ensuremath{\Omega}$), the magnitude of the spin spiral rises rapidly to a value of order 1 (independent of $\ensuremath{\Omega}$). Moreover, near $g=+\ensuremath{\infty}$, the spins of neighboring fermions can interfere destructively due to quantum fluctuations of particle motion, strongly distorting the spin spiral and pulling the spins substantially away from the direction of the local field at various locations. These effects are consequences of the spin-charge separation in the strongly repulsive limit. They will also occur in other 1D quantum gases with higher spins.
Strongly interacting many-body systems remain a central challenge of modern physics. Recent developments in the field of ultra-cold atomic physics have opened a new window onto this enduring problem. Experimental progress has revolutionized the approach to studying many-body systems and the exotic behaviors that emerge in these systems. It is now possible to engineer and directly measure a variety of models that can capture the essential features of real materials without the added complexity of disorder, impurities, or complicated or irregular geometries. The parameters of these models can be freely tuned with tremendous precision. These experimental realizations are an ideal setting in which to test and calibrate computational many-body methods that can provide insight and quantitative understanding to many of the open questions in condensed matter and many-body physics. in this thesis we study several models of strongly interacting many-fermion systems using cutting-edge numerical techniques including Hartree-Fock-Bogoliubov (HFB) mean-field theory and auxiliary-field quantum Monte Carlo (AFQMC). We explore the exotic phases and behaviors that emerge in these systems, beginning with finite-momentum pairing states in attractive spin-polarized fermions. We next demonstrate the unique capability of AFQMC to treat systems with spin-orbit coupling (SOC). We obtain high-precision, and in many cases numerically exact, results on SOC systems that can eventually be compared directly to experiment. The first system we highlight is the attractive Fermi gas with Rashba SOC, which displays unconventional pairing, charge, and spin properties. We then study the coexistence of charge and superfluid order, as well as topological signatures, in attractive lattice fermions with Rashba SOC. Our results provide a new, high-accuracy understanding of a strongly interacting many-body system and its exotic behaviors. These techniques can serve as a general framework for the treatment of strong interactions and SOC in many-body systems, and provide a foundation for future work on exotic phases in models and real materials.
Motivated by recent experimental development, we investigate spin–orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate the momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin–orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here spin rotating means the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle Finally, we show that the momentum k peak , at which the peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived, which suggests that the predicted spin-rotating ferromagnetic ( k peak < π /2 ) and antiferromagnetic ( π /2 < k peak < π ) correlations can be detected experimentally by measuring the SOC-dependent spin-structure factor via time-of-flight imaging.