Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders

Submission summary

 As Contributors: Federico Becca · Arianna Montorsi · Luca Fausto Tocchio Arxiv Link: https://arxiv.org/abs/1810.12268v2 (pdf) Date accepted: 2019-01-28 Date submitted: 2019-01-23 01:00 Submitted by: Tocchio, Luca Fausto Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approaches: Theoretical, Computational

Abstract

Short-range antiferromagnetic correlations are known to open a spin gap in the repulsive Hubbard model on ladders with $M$ legs, when $M$ is even. We show that the spin gap originates from the formation of correlated pairs of electrons with opposite spin, captured by the hidden ordering of a spin-parity operator. Since both spin gap and parity vanish in the two-dimensional limit, we introduce the fractional generalization of spin parity and prove that it remains finite in the thermodynamic limit. Our results are based upon variational wave functions and Monte Carlo calculations: performing a finite size-scaling analysis with growing $M$, we show that the doping region where the parity is finite coincides with the range in which superconductivity is observed in two spatial dimensions. Our observations support the idea that superconductivity emerges out of spin gapped phases on ladders, driven by a spin-pairing mechanism, in which the ordering is conveniently captured by the finiteness of the fractional spin-parity operator.

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Published as SciPost Phys. 6, 018 (2019)

Dear Editor,

we resubmit the revised version of the manuscript, where we addressed the questions and comments raised by the referees.
We already provided a reply to both referees and we will give a point-by point list of changes in the next section.

Luca F. Tocchio, on behalf of all the authors

List of changes

-) The affiliation of the second author is now changed.
-) In Fig.1, we clarified that the value of the critical density where superconducting correlations start to develop in the 2D case
is obtained from a fully 2D numerical calculation.
-) We included the error bars in Fig. 5 and we specified that the error bars are smaller than the symbol size in Figs. 2, 3, 4, 6, and 7.
-) We wrote explicitly the band dispersion and the pairing terms in Eq.(7).
-) We clarified the choice of boundary conditions, at the end of the Variational Monte Carlo method section.
-) We expanded the last paragraph of the conclusions and we included two extra references (Refs. 47 and 48),
following the suggestion of the second referee.
-) We updated the acknowledgements.