Superconductivity in lightly doped Hubbard model on honeycomb lattice

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Superconductivity in lightly doped Hubbard model on honeycomb lattice".

Mira: Here's the gist of the paper. The gist The ground state of lightly doped Hubbard model on long three- and four-leg cylinders suggests that it is consistent with a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders, both decaying as a power law at long distances with corresponding exponents Ksc < 2 and Kc < 2 Model and Method The study utilizes large-scale density-matrix renormalization group (DMRG) simulations to investigate the ground state properties of the lightly doped single-band Hubbard model on the honeycomb lattice across long three- and four-leg cylinders.

Kai: The Hamiltonian considered is defined as H = - t X h i j i σ cˆ† i σ cˆj σ + h.c.

Mira: + U X i nˆi↑nˆi↓ (1).

Kai: The lattice geometry is cylindrical, with periodic boundary condition along the e2 = (1/2, √3/2) direction and open boundary condition along the e1 = (1, 0) direction.

Paper summary: Kai: So, to recap, this paper studies the lightly doped Hubbard model on long three- and four-leg cylinders using large-scale density-matrix renormalization group simulations. The main finding is that the ground state matches a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders.

Mira: What's important about those orders is that they decay as power laws at long distances, specifically with exponents K sc and K c both being less than two <ref:2303.12348#pg1>.

Lev: So, the naive question a listener might have is why are these specific exponents less than two instead of just being exactly two <ref:2303.12348#pg1>?

Kai: Well, the paper finds that this power law decay for superconductivity implies a superconducting susceptibility that diverges as T approaches zero, specifically chi about T minus (two-K sc) > <ref:2303.12348#pg1>

Mira: That divergence is what makes it quasi-long-range rather than true long-range order. It's about the nature of the correlation itself.

Lev: For us on the ground, this means that if we were to try and build a real quantum computer using this physics, we'd have to deal with these algebraic decay rates when calculating things like susceptibility or correlation functions over large distances.

Kai: It matters because it connects the Hubbard model—which is believed to capture low-energy physics of cuprate superconductors

one–three: —to these specific types of emergent order <ref:2303.12348#pg1>.

Mira: And this result is interesting because the pairing symmetry they see is consistent with what you’d expect from a nematic d-wave, which reminds people of the plaquette d-wave seen on four-leg square cylinders.

Lev: But they point out that their specific setup, using only nearest-neighbor hopping terms for the Hubbard model, is different from studies on square or triangular lattices.

Kai: Exactly. So it’s this finding that quasi-long-range superconductivity can happen in the lightly doped Hubbard model with just nearest-neighbor electron hopping matrix.

Mira: And they are looking at this on geometries like three and four-leg cylinders, which is a specific way to probe these effects without needing infinite lattices.

Conclusion: Kai: So, looking at the full title, "Superconductivity in lightly doped Hubbard model on honeycomb lattice," it really sets up a picture of complex, competing orders coexisting.

Mira: The authors Cheng Peng, D. N. Sheng and Hong-Chen Jiang are using large-scale density-matrix renormalization group studies on long three- and four-leg cylinders to find this specific ground state structure.

Lev: From an engineering standpoint, the implication is that if we want to model real materials like cuprates, we can't just look for a simple phase transition; we have to account for these competing power-law decays in the superconducting and charge density wave sectors.

Kai: It means that when you tune parameters in the Hubbard model, especially doping delta, you are tuning not just whether superconductivity exists, but how it coexists with other structural orders like the charge density wave.

Mira: The main implication for me is that this confirms a specific type of emergent behavior in these strongly correlated systems where both pairing and charge modulation show algebraic decay at long scales.

Lev: For error correction research, this tells us that the low-energy physics we are modeling has these inherent correlation functions, and we have to design codes that respect those power-law decay rates instead of assuming simpler exponential behavior everywhere.

Kai: It's about realizing that the superconducting state in this model isn't just one thing; it has these other components—the CDW—that are intricately linked through these power-law interactions.

Mira: So, the paper shows a specific landscape for lightly doped Hubbard models where quasi-long-range superconductivity and charge density wave orders exist together under specific conditions.

Lev: It’s a solid piece of physics showing how complex the ground state can be even in this relatively simple effective model.