Abstract
Competing and intertwined orders including inhomogeneous patterns of spin and charge are observed in many correlated electron materials, such as high-temperature superconductors. Introducing a new development of the constrained-path auxiliary-field quantum Monte Carlo method, we study the interplay between thermal and quantum fluctuations in the two-dimensional Hubbard model. We obtain an accurate and systematic characterization of the evolution of the spin and charge correlations as a function of temperature T and how it connects to the ground state, at three representative hole doping levels δ=1/5, 1/8, and 1/10. We find increasing short-range commensurate antiferromagnetic correlations as T is lowered. As the correlation length grows sufficiently large, a modulated spin-density wave (SDW) appears. At δ=1/5 and U/t=6, the SDW saturates and remains short-ranged as T→0. In contrast, at δ=1/8, 1/10 and U/t=8, this evolves into a ground-state stripe phase. We study the relation between spin and charge orders and find that formation of charge order appears to be driven by that of the spin order. We identify a finite-temperature phase transition below which charge ordering sets in and discuss the implications of our results for the nature of this transition.
| Original language | English |
|---|---|
| Article number | 011007 |
| Journal | Physical Review X |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2023 |
| Externally published | Yes |
Funding
We thank Richard Scalettar and Fedor Šimkovic for carefully reading the manuscript and insightful suggestions. We are also grateful to Michel Ferrero, Edwin Huang, Andrew Millis, Subir Sachdev, and Hao Xu for very useful discussions. Y.-Y. H. acknowledges the National Natural Science Foundation of China under Grant No. 12047502. The Flatiron Institute is a division of the Simons Foundation.