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Science

Spin and charge go their separate ways

Jelena Stajic

Published Jan 9, 2020• 0 citations
Publisher

Abstract

Quantum Simulation Strongly interacting chains of fermions are predicted to exhibit two types of collective excitations: spinons, which carry only spin, and holons, which carry only charge. These excitations move at different velocities. Signatures of this so-called spin-charge separation have been observed in solid-state systems, but obtaining direct dynamical evidence is tricky. With this goal in mind, Vijayan et al. perturbed a chain of ultracold interacting fermions housed in a one-dimensional optical lattice by removing one of the atoms. This gave rise to two independent excitations, which the researchers identified as spinons and holons using a quantum gas microscope. Science , this issue p. [186][1] [1]: /lookup/doi/10.1126/science.aay2354

DOI
10.1126/science.367.6474.158-d

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Quantum Simulation
Strongly interacting chains of fermions are predicted to exhibit two types of collective excitations: spinons, which carry only spin, and holons, which carry only charge. These excitations move at different velocities. Signatures of this so-called spin-charge separation have been observed in solid-state systems, but obtaining direct dynamical evidence is tricky. With this goal in mind, Vijayan et al. perturbed a chain of ultracold interacting fermions housed in a one-dimensional optical lattice by removing one of the atoms. This gave rise to two independent excitations, which the researchers identified as spinons and holons using a quantum gas microscope.
Science , this issue p. 186
Quantum Magnetism Strongly interacting electrons lined up along a string can experience the so-called spin-charge separation, where the electrons “split” into effective carriers of spin and charge, which then move independently. This phenomenon has been observed, somewhat indirectly, in solids. Hilker et al. show spin-charge separation in a direct way by using a one-dimensional (1D) array of cold atoms, playing the role of electrons, whose degrees of freedom of spin and charge can be monitored using a fermionic quantum gas microscope. Empty sites in the 1D lattice moved freely without disturbing the underlying antiferromagnetic order. Science , this issue p. [484][1] [1]: /lookup/doi/10.1126/science.aam8990
Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings.
We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.
Quantum Simulation Ultracold atomic gases are very good at simulating electrons in solids but lack one essential party trick: charge. Their neutrality makes it challenging to simulate phenomena such as the quantum Hall effect, which, in the case of charged electrons, is easily induced by an external magnetic field. One way to produce a similar effect in a neutral system is to rotate it, but achieving the equivalent of strong magnetic fields remains difficult. Fletcher et al. rotated a gas of trapped sodium atoms, reaching a state in which the gas could be described by a single lowest Landau-level wave-function. The system is expected to be a testbed for studying the behavior of strongly interacting many-body states. Science , aba7202, this issue p. [1318][1] [1]: /lookup/doi/10.1126/science.aba7202
Quantum Simulation Much can be learned about the nature of a solid from how charge and spin propagate through it. Transport experiments can also be performed in quantum simulators such as cold atom systems, in which individual atoms can be imaged using quantum microscopes. Now, two groups have investigated transport in the so-called Fermi-Hubbard model using a two-dimensional optical lattice filled with one fermionic atom per site (see the Perspective by Brantut). Moving away from half-filling to enable charge transport, Brown et al. found that the resistivity had a linear temperature dependence, not unlike that seen in the strange metal phase of cuprate superconductors. In a complementary study on spin transport, Nichols et al. observed spin diffusion driven by superexchange coupling. Science , this issue p. [379][1], p. [383][2]; see also p. [344][3] [1]: /lookup/doi/10.1126/science.aat4134 [2]: /lookup/doi/10.1126/science.aat4387 [3]: /lookup/doi/10.1126/science.aaw1326