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arXiv:2305.09529 · Physical Review Research

Spin-charge correlations in finite one-dimensional multiband Fermi systems

Judith Becker, Georgios M. Koutentakis, Peter Schmelcher

Published Oct 12, 2023• 3 citations
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Abstract

We investigate spin-charge separation of a spin-$\frac{1}{2}$ Fermi system confined in a triple well where multiple bands are occupied. We assume that our finite fermionic system is close to fully spin polarized while being doped by a hole and an impurity fermion with opposite spin. Our setup involves ferromagnetic couplings among the particles in different bands, leading to the development of strong spin-transport correlations in an intermediate interaction regime. Interactions are then strong enough to lift the degeneracy among singlet and triplet spin configurations in the well of the spin impurity but not strong enough to prohibit hole-induced magnetic excitations to the singlet state. Despite the strong spin-hole correlations, the system exhibits spin-charge deconfinement allowing for long-range entanglement of the spatial and spin degrees of freedom.

DOI
10.1103/physrevresearch.5.043039

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We investigate spin-charge separation of a spin-12\frac{1}{2}21​ Fermi system confined in a triple well where multiple bands are occupied. We assume that our finite fermionic system is close to fully spin polarized while being doped by a hole and an impurity fermion with opposite spin. Our setup involves ferromagnetic couplings among the particles in different bands, leading to the development of strong spin-transport correlations in an intermediate interaction regime. Interactions are then strong enough to lift the degeneracy among singlet and triplet spin configurations in the well of the spin impurity but not strong enough to prohibit hole-induced magnetic excitations to the singlet state. Despite the strong spin-hole correlations, the system exhibits spin-charge deconfinement allowing for long-range entanglement of the spatial and spin degrees of freedom.
In this letter we consider a magnetic impurity in a one-dimensional spin-1/21/21/2 Fermi gas with infinitely strong repulsive interaction between fermions. We rigorously prove that, independent of whether the magnetic coupling between impurity and fermions is ferromagnetic or anti-ferromagnetic, the ground state is always a fully polarized ferromagnetic state for the itinerant fermions. This ferromagnetism can be understood as a cooperative effect of avoiding frustration of magnetic coupling during fermion hopping and the large spin degeneracy of a fermion Tonks gas. By numerically diagonalizing a finite size system, we show that the spin gap first increases linearly with magnetic coupling strength in the weak coupling regime, while decreases in the strong coupling regime. Our results show that a magnetic impurity in a strongly correlated gas can exhibit effect different from the Kondo effect as in a weakly correlated Fermi liquid.
Different models for doping of two-orbital chains with mobile S=1/2S=1/2S=1/2 fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.
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.
Abstract The emission of two correlated fermions from a nuclear, or, in general, quantum meta-stable system is a poorly known, but fundamental problem: the interaction between the fermions can significantly affect the tunneling process. The behaviour of spin-singlet or spin-triplet emission has not been fully studied. In this article, the one-dimensional tunneling process of two fermions of the same kind is investigated. We solve the time-dependent Schrödinger equation for the two-fermion (2F) state, which is initially confined inside the square-well-plus-barrier potential. The interaction between the two fermions is schematically described by a short-range square-well attractive potential. A noticeable difference between the spin-singlet and triplet emissions is shown. Their tunneling probability, which is evaluated from the time-dependent survival probability, depends on the total spin, even if the effective-barrier height is fixed to be equivalent. Also, a spatial correlation of two fermions appears (vanishes) in the spin-singlet (triplet) case. The total-spin dependence of 2F emission can be attributed to the anti-symmetrization condition: it allows (prohibits) degenerate pairing, where two fermions can occupy the same spatial orbit, in the spin-singlet (triplet) case. This degenerate pairing makes the spin-singlet 2F state more long-lived than the spin-triplet one, even under the equivalent conditions. Only in the spin-singlet channel, the short-range 2F attraction enhances the degenerate-pair component, providing the difference between correlated and uncorrelated emissions. On the other hand, the spin-triplet emission cannot profit from the 2F interaction, due to the Pauli principle. These conclusions are independent of the physical scales.
We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.
Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model.