Stripe order in the underdoped region of the two-dimensional Hubbard model

Abstract

† These authors contributed equally to the calculations in this work.Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The twodimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find 1 arXiv:1701.00054v3 [cond-mat.str-el]

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

“…It can be observed that the wavelength that gives the lowest energy depends on the doping and increases towards half-filling, which is expected from mean-field theory [34]. Zheng et al [43] studied the same model using different numerical methods at doping 0.125. There it was found that the lowest energy stripe state is given by a wavelength of λ ≈ 8 for U = 6 and 8.…”

“…We find a wide region of coexistence between striped order and spatially modulated d-wave superconductivity, and analyze the behavior of the superconducting order parameter in the striped states. Compared to other recent ground-state studies, we can reach longer stripe wavelengths [44] and study a wider doping region [43]. This allows us to more carefully study the stripe energetics and to determine the ground-state stripe wavelengths.…”

“…However, its interplay with the d-wave superconductivity has not yet been thoroughly explored. At the fixed doping 1 8 , superconducting states were found within DMET, iPEPS, and DMRG, but the states seemed to be metastable [43]. The topic has also been touched in other DMET [44] and functional renormalization group calculations [68], as well as in variational calculations of finite width chains [44,69], but has not been taken into consideration in the DMFT-based Green's function methods.…”

“…Because the unit cell is always of even length, we only study stripe states of even periodicity. For compatibility with existing numerical literature [43], we define the stripe wavelength λ as half the wavelength of the staggered magnetization, so that λ = N c .…”

“…These include the density matrix embedding theory (DMET) [39], constrained path auxiliary field Monte Carlo (AFQMC) [40], the tensor network wave function ansatz based iPEPS [41], and advances in the density matrix renormalization group method (DMRG) to handle wider quasi-2D systems [42]. A study comparing these four methods consistently found striped states at 1 8 doping [43]. The DMET has also been used to map the density-interaction phase diagram of the Hubbard 2469-9950/2018/97(7)/075112 (10) 075112-1 ©2018 American Physical Society model showing (co)existence of stripe states and d-wave superconductivity [44], and AFQMC has been used to study long wavelength stripes at low doping [45].…”