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Pairwise entanglement, charge-spin separation, and the Mott transition for correlated electrons in nanochains

Adam Rycerz

Published Nov 3, 2016• 0 citations
OpenAlex

Abstract

Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization - ab initio method (EDABI), for chains containing $N\leqslant{}16$ hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for $N\leqslant{}20$ shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with $1/N\rightarrow{}0$ vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.

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Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization - ab initio method (EDABI), for chains containing N⩽16N\leqslant{}16N⩽16 hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for N⩽20N\leqslant{}20N⩽20 shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with 1/N→01/N\rightarrow{}01/N→0 vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.
Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization— ab initio , for chains containing hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.
We overview the EDABI method developed recently and combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localization-delocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show, that, the statistical distribution function for electrons in a nanochain evolves from the Fermi-Dirac-like to the Luttinger-liquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresponds to the HOMO-LUMO splitting in the molecular and organic solid states. Also, the nanochains exhibit magnetic splitting (Slater-like), even without the symmetry breaking, since the spin-spin correlations extend over the whole system. Thus, the correlated nanoscopic systems exhibit unique and universal features, which differ from those of molecular and infinite systems. These features define unique properties reflecting "the Mott physics" on the nanoscale. We also employ the EDABI method to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.
We implement the recently proposed approach combining Exact Diagonalization in the Fock space with an Ab Initio method (EDABI) to obtain a fairly complete description of correlated nanochains. In particular, the microscopic parameters are determined and the evolution of the system properties is traced in a systematic manner as a function of the interatomic distance. Both ground‐state and dynamical correlation functions are discussed within a single scheme. The principal physical results are: (i) the appearance of mixed metallic and insulating features for a one‐dimensional nanochain in the half‐filled band case, and (ii) the transformation from a highly‐conducting nanometal to the charge‐ordered nanoinsulator away from the half‐filling. The analysis is performed using the Gaussian 1s‐like basis and includes long‐range Coulomb interactions.
We study quantum entanglement in a single–level quantum dot in the linear– response regime. The results show, that the maximal quantum value of the conductance 2e 2 /h not always match the maximal entanglement. The pairwise entanglement between the quantum dot and the nearest atom of the lead is also analyzed by utilizing the Wootters formula for charge and spin degrees of freedom separately. The coexistence of zero concurrence and the maximal conductance is observed for low values of the dot–lead hybridization. Moreover, the pairwise concurrence vanish simultaneously for charge and spin degrees of freedom, when the Kondo resonance is present in the system.
Interacting one-dimensional electron systems are generally referred to as "Luttinger liquids", after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The "spin-incoherent Luttinger liquid" describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale, and it is realized for instance in the strongly interacting Hubbard chain (with U → ∞). Similar physics can take place in the ground-state, when a Luttinger Liquid is coupled to a spin bath, which effectively introduces a "spin temperature" through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be exactly written as a factorized wave-function, with a spin wave-function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled t-J chains, but also for the t-J-Kondo chain with strongly interacting conduction electrons. In chapter 3 we argue that this theory is quite universal and may describe a family of problems that could be dubbed "spin-incoherent".
We apply our new method of approach to electronic states in correlated systems [for a brief review, Part I, see: Acta Phys. Pol. B31, 2879 (2000)] to the analysis of the states and electron localization in nanoscopic chains containing up to N = 12 atoms. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. We also define the many-particle wave function and calculate it explicitly for the hydrogen molecule. Further applications of our method are listed at the end.