Abstract
The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally entangled typical thermal states method on width-four cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature and is accompanied by a steplike feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature.
- Received 12 October 2020
- Revised 24 March 2021
- Accepted 11 May 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031007
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
A collection of interacting electrons in a solid can form a metal, exhibit magnetism, or become a superconductor. Since all these effects are relevant for technological applications, it is important to understand the mechanisms behind them. Here, we use a relatively new computational method to study a foundational model of superconductivity to see how the behavior of interacting electrons changes as temperature increases.
The Hubbard model is a simplified description of electrons in a solid that is believed to capture the essential electronic properties of many materials, including the high-temperature copper oxide, or cuprate, superconductors. However, despite long attempts to solve this model, understanding its phase diagram remains one of the most challenging and interesting endeavors in theoretical condensed-matter physics.
Using the recently developed “minimally entangled typical thermal state” computational technique to study this model, we make several interesting observations. When there are fewer electrons than lattice sites, we observe that the density of electrons forms a regular wavelike pattern. Upon increasing the temperature, this pattern melts, and we find a tendency of the system to order antiferromagnetically, which means that the spins of neighboring electrons prefer to point in opposite directions. Importantly, we find that in this regime, the system shares many features with the experimentally observed pseudogap regime of the cuprate superconductors.
Demonstrating the feasibility of this new kind of simulation paves the way toward understanding several most puzzling phenomena in solid-state physics, such as high-temperature superconductivity or strange metals.
