Large Isolated Stripes on Short 18-leg $t$-$J$ Cylinders

Spin-charge stripes belong to the most prominent low-temperature orders besides superconductivity in high-temperature superconductors. This phase is particularly challenging to study numerically due to finite-size effects. By investigating the formation of long, isolated stripes, we offer a perspective complementary to typical finite-doping phase diagrams. We use the density-matrix renormalization group algorithm to extract the ground states of an 18-leg cylindrical strip geometry, making the diameter significantly wider than in previous works. This approach allows us to map out the range of possible stripe filling fractions on the electron versus hole-doped side. We find good agreement with established results, suggesting that the spread of filling fractions observed in the literature is governed by the physics of a single stripe. Taking a microscopic look at stripe formation, we reveal two separate regimes - a high-filling regime captured by a simplified squeezed-space model and a low-filling regime characterized by the structure of individual pairs of dopants. Thereby, we trace back the phenomenology of the striped phase to its microscopic constituents and highlight the different challenges for observing the two regimes in quantum simulation experiments.

💡 Research Summary

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This paper tackles one of the most persistent challenges in the numerical study of cuprate high‑temperature superconductors: the reliable identification of spin‑charge stripe order in the presence of severe finite‑size effects. The authors adopt a novel geometry—a short, 18‑leg cylindrical lattice (4 × 18 sites)—and apply the density‑matrix renormalization group (DMRG) within the matrix‑product‑state (MPS) framework. By employing a tailored MPS mapping that shifts the exponential cost from the periodic (y) direction to the open (x) direction, they make the computation of such a wide cylinder comparable in effort to conventional 8‑leg cylinders.

The model investigated is the t‑t′‑J Hamiltonian with nearest‑neighbor hopping t = 1 (energy unit), next‑nearest‑neighbor hopping t′∈