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arXiv:1011.1782

Quantum decoherence in strongly correlated electron systems

Byung Gyu Chae

Published Nov 8, 2010• 1 citation
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Abstract

Complexity in strongly correlated electron systems is analyzed by considering decoherence process between the localized state, |L> and the itinerant state, |I>. The coherent superposition state of a|I> + b|L> decoheres to the pointer states in the proximity of both extremes of the correlation where the symmetry-breaking ground states of the charge pairing emerge. For maximizing the entropy of the system, the superconducting pairing and the spin density wave coexist within the uncertainty principle, which invokes the metastable states as like pseudogap phase and electronic inhomogenity.

DOI
10.48550/arxiv.1011.1782

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Complexity in strongly correlated electron systems is analyzed by considering decoherence process between the localized state, |L> and the itinerant state, |I>. The coherent superposition state of a|I> + b|L> decoheres to the pointer states in the proximity of both extremes of the correlation where the symmetry-breaking ground states of the charge pairing emerge. For maximizing the entropy of the system, the superconducting pairing and the spin density wave coexist within the uncertainty principle, which invokes the metastable states as like pseudogap phase and electronic inhomogenity.
The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.
The strong interaction between electrons reveals the duality of the itinerancy and the localization of quasiparticles. The physical phenomena corresponding to each component of the duality could be realized and coexist within the category of the uncertainty principle of the carrier dynamics, which can be a strong reason of the complexity appearing in the strongly correlated system. A possible mechanism for the high-temperature superconductivity is proposed on the basis of the interplay between the renormalized expectation quantities of both parts.
We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local ddd-wave or sss-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions VSV^{S}VS that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions HSBH^{SB}HSB that lead to decoherence influence the correlation energy. The effects only decouple when [VS,HSB]=[HS,HSB]=0[V^{S},H^{SB}]=[H^{S},H^{SB}]=0[VS,HSB]=[HS,HSB]=0, where HSH^{S}HS is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.
In the presence of interactions with the environment, decoherence selects stable classical states, the pointer states, while suppressing arbitrary macroscopic coherent superpositions. In close analogy, the metastable symmetry-breaking ground states of many-body Hamiltonians should be the ones with the least macroscopic entanglement and thus the most classical ones among all possible quantum ground states. By considering the mutual information based on the 2-Renyi entanglement entropy and using a locality result, we show that symmetry-breaking states have the least macroscopic entanglement and, consequently, that they are the ones selected in real world by environmental decoherence.