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 (METTS) method on width $4$ 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 $T/t \approx 0.05$ and is accompanied by a step-like feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $\mathbf{k}=(\pi/2, \pi/2)$ 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.
Highlights
Understanding the physics and phase diagram of copperoxide high-temperature superconductors is arguably one of the most fundamental and challenging problems in modern condensed matter physics [1,2,3,4,5]
The results from the minimally entangled typical thermal states (METTS) simulations presented in the previous sections yield several interesting new insights into the physics of the Hubbard model in the strongcoupling regime at U=t 1⁄4 10 at finite temperature
Even though the exact value of U=t 1⁄4 10 and p 1⁄4 1=16 is not included in the results of these authors, their phase diagrams suggest that this point realizes what is referred to as the Luther-Emery 1 (LE1) phase at T 1⁄4 0
Summary
Understanding the physics and phase diagram of copperoxide high-temperature superconductors is arguably one of the most fundamental and challenging problems in modern condensed matter physics [1,2,3,4,5]. Cluster extensions of dynamical mean-field theory (DMFT) [43,44,45,46], on the other hand, address the problem from a different perspective These methods use the degree of spatial locality as a control parameter and, starting from the high-temperature limit in which the physics is highly local, follow the gradual emergence of nonlocal physics as spatial correlations grow upon reducing the temperature. It has been argued that for certain onedimensional systems, where entropy scaling is less important than the sampling error, the METTS algorithm does not outperform the purification approach [80] In this manuscript, we develop and refine the METTS methodology and demonstrate that it can be successfully applied to study the finite-temperature properties of the doped Hubbard model in the strong-coupling limit on a width-four cylinder. We demonstrate that the variance of several estimators quickly decreases when lowering temperatures as well as increasing system sizes
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