Good news!
"By cleverly applying a computational technique, scientists have made a breakthrough in understanding the ‘pseudogap,’ a long-standing puzzle in quantum physics with close ties to superconductivity. The discovery ... will help scientists in their quest for room-temperature superconductivity ...
By better understanding how the pseudogap appears and how it relates to the theoretical properties of the superconductive materials at absolute zero, scientists are getting a clearer picture of those materials ..."
Certain materials involving copper and oxygen display superconductivity (where electricity flows without resistance) at relatively high — but still frigid — temperatures below minus 140 degrees Celsius. At higher temperatures, these materials fall into what’s called the pseudogap state, where they sometimes act like a normal metal and sometimes act more like semiconductors. Scientists have found that the pseudogap shows up in all so-called high-temperature superconducting materials. But they didn’t understand why or how it shows up, or if it sticks around as the temperature drops to absolute zero (minus 273.15 degrees Celsius), the unreachable lower limit of temperature at which molecular motion stops.
From the editor's summary and abstract:
"Editor’s summary
Despite its simplicity, the Hubbard model may be capable of describing some instances of strongly correlated matter. However, this remains difficult to solve numerically; connecting the results at zero and finite temperatures is particularly tricky. ... used diagrammatic Monte Carlo calculations to examine the appearance of the pseudogap phase in the doped Hubbard model at finite temperatures. This phase was found to be closely associated with antiferromagnetic spin correlations and to connect to the ground-state stripe phase calculated at zero temperature. ...
Structured Abstract
INTRODUCTION
Large systems of interacting quantum particles host a wealth of collective phenomena, such as superconductivity, magnetism, and metal-insulator transitions. Prominent examples are materials with strong correlations between electrons, such as transition metal oxides and twisted bilayer graphene, and ultracold atomic gases trapped in optical lattices. Understanding these systems is a formidable theoretical and computational challenge, with implications both for fundamental physics and for the design of new functional materials. One of the unusual states of matter observed in these systems is the so-called “pseudogap” regime in which the electronic excitations of a metal are suppressed in a selective manner depending on their momentum. A central open question is whether such a peculiar state can exist down to low temperature without intervening long-range orders being formed.
RATIONALE
The Fermi-Hubbard model, introduced in 1963, established itself as a fundamental theoretical platform to investigate interacting quantum systems. Despite its formal simplicity, it may be capable of capturing the essence of strongly correlated materials. In the absence of an analytical solution, it has been the subject of numerous computational studies, but it still eludes a controlled solution in its most notable regimes at finite temperature. The main obstacles come from the exponentially large size of the configuration space and the so-called fermionic sign problem that most algorithms suffer from, hence impeding the simulation of large systems. In this work, we used a state-of-the-art unbiased computational algorithm, diagrammatic Monte Carlo, to obtain controlled results in nontrivial regimes of the Fermi-Hubbard model on an infinite two-dimensional square lattice. We provide answers to some outstanding questions regarding the origin and fate of the pseudogap state as temperature is lowered for a broad range of values of the model parameters. We benchmark our results against several other numerical methods, including dynamical mean-field theory and its cluster extensions.
RESULTS
Our calculations identified three distinct physical regimes as a function of temperature and electronic density: a weakly correlated metal, a strongly correlated metal, and a pseudogap regime. The formation of the pseudogap is associated with the onset of antiferromagnetic spin correlations. At weak coupling, they are long ranged, whereas their spatial extent becomes shorter at strong coupling. As these correlations develop, a deformation of the Fermi surface is first observed at intermediate densities in the strongly correlated metal. At densities closer to one electron per site, the coherence of electronic excitations for “antinodal” momenta close to the Brillouin zone boundary is suppressed, and a pseudogap appears. In this regime, the self-energy that quantifies the modification of the dispersion and lifetime of electronic excitations by interactions develops a quasi-pole. We show how spin fluctuation theory can be modified to provide a good description of the nonlocal part of the self-energy both in the weak and strong coupling regimes. In contrast to spin correlations, we did not observe the development of sizable charge correlations associated with the pseudogap in the temperature regimes accessible to our method. We addressed the fate of the pseudogap at low temperature by performing an extrapolation of the pseudogap region to zero temperature. We show that the range of density and coupling strength where a pseudogap is found in this limit precisely coincides with that in which ground-state studies find a stripe phase with long-range spin and charge order.
CONCLUSION
We have obtained controlled results that highlight the crucial role of spin correlations in driving the formation of the pseudogap. Eventually, this state becomes unstable and, in the absence of a next-nearest-neighbor hopping, turns into a stripe phase. This result and the corresponding handshake between finite and zero-temperature methods is a major achievement of our work. We have further demonstrated the robustness of our findings by investigating the pseudogap for a nonzero next-nearest-neighbor hopping and have observed a similar finite-temperature behavior. In this case, further work involving controlled ground-state studies will be necessary to clarify the fate of the pseudogap at low temperature, which remains an outstanding question."
The low-doping regime of the Hubbard model with nearest-neighbor hopping.
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