Collective quantum tunneling of strongly correlated electrons in commensurate mesoscopic rings

Abstract

We present a new effect that is possible for strongly correlated electrons in commensurate mesoscopic rings: the collective tunneling of electrons between classically equivalent configurations, corresponding to ordered states possessing charge and spin density waves (CDW, SDW) and charge separation (CS). Within an extended Hubbard model at half filling studied by exact numerical diagonalization, we demonstrate that the ground state phase diagram comprises, besides conventional critical lines separating states characterized by different orderings (e.g. CDW, SDW, CS), critical lines separating phases with the same ordering (e.g. CDW-CDW) but with different symmetries. While the former also exist in infinite systems, the latter are specific for mesoscopic systems and directly related to a collective tunnel effect. We emphasize that, in order to construct correctly a phase diagram for mesoscopic rings, the examination of CDW, SDW and CS correlation functions alone is not sufficient, and one should also consider the symmetry of the wave function that cannot be broken. We present examples demonstrating that the jumps in relevant physical properties at the conventional and new critical lines are of comparable magnitude. These transitions could be studied experimentally e.g. by optical absorption in mesoscopic systems. Possible candidates are cyclic molecules and ring-like nanostructures of quantum dots. PACS. 71.45.Lr Charge-density-wave systems -75.30.Fv Spin-density waves -72.15.Nj Collective modes (e.g., in one-dimensional conductors -73.20.Mf Collective excitations (including excitons, polarons, plasmons and other charge-density excitations)

Alternation of Singlet and Triplet States in Carbon‐Based Chain Molecules and Its Astrochemical Implications: Results of an Extensive Theoretical Study

“…In this paper, we demonstrated that, in families of carbon‐based chains, most stable members of one parity (even or odd) are singlets while most stable members of the opposite parity (odd or even) are triplets. This is a sui generis effect qualitatively different from other even–odd effects known from studies over decades in other areas …”

“…Noteworthily, the even-odd singlet-triplet alternation 25 extensively discussed in this paper is qualitatively different from all other even-odd effects (e.g., in multilayers, 26 self-assembled monolayers, 27 quantum dot arrays, [28][29][30][31] molecular electronic devices 2,3 ) known since the early days of quantum mechanics. [32][33][34][35] In those cases, it is merely a certain property rather than the very nature of the ground state that exhibits alternation.…”

Phase separation and electron pairing in repulsive Hubbard clusters

“…Such ensemble averages have been demonstrated to be relevant for nanoclusters. 20 Although there have been numerous studies of phase separation and similar phenomena in Hubbard systems, 16,21 in our opinion, thermal properties and phase instabilities of small Hubbard clusters at an arbitrary filling have not been fully explored.…”

Reply to “Comment on ‘Critical analysis of a variational method used to describe molecular electron transport’”

“…4 are described by Hamiltonians H(ε g ) possessing a particlehole (or charge conjugation) symmetry (see, e. g., Ref. 13 and citations therein) around ε g = 0: H h (ε g ) = H(−ε g ). That is, the zero-bias conductance g(+ε g ) = g(−ε g ) (as well as other relevant properties not considered in Ref.…”