Competing States in thet-JModel: Uniformd-Wave State versus Stripe State

Abstract

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with antiphase d-wave order. The optimal stripe filling is not constant but increases with J=t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.

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

“…While this state is not the ground state in the present case, it is still conceivable that the ground state exhibits this behavior in some part of the U -doping phase diagram. This has been seen, e.g., in studies of the t-J model, using a variational tensor network ansatz for the ground state [46].…”

“…Similarly, for the d-wave superconductivity we have used an ansatz of the in-phase type, where ⊥ has the same sign throughout the whole unit cell. In previous studies of the Hubbard and t-J models where d-wave order is found, this type is usually found to be most stable [43,44,46], although the antiphase type where a sign change occurs can also be close in energy [46].…”

“…In this work, we have studied the so-called vertical stripes, where the direction of the spatial modulation is along the lattice bonds. This is the type of stripe state that is usually found to have lowest energy [43,46,81], although the difference to striped order in the diagonal direction can be very small [46,62,81]. Similarly, for the d-wave superconductivity we have used an ansatz of the in-phase type, where ⊥ has the same sign throughout the whole unit cell.…”

“…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]. The existence of the stripe state is also being debated for the closely related t-J -model, where stripes have been studied using iPEPS [46], variational monte carlo [47], and fixed-node Monte Carlo (FN) methods [48]. The dynamical mean-field theory (DMFT) with its cluster extensions is another relatively recent, although already well established, numerical method [49][50][51].…”

Doping asymmetry and striping in a three-orbitalCuO2Hubbard model

“…One-band Hubbard and t-J models have been found, within various approximations, to exhibit striped charge and spin structures [19][20][21][22][23][24] , modulated nematic phases [25][26][27] as well as pair density wave phases [28][29][30] . RPA calculations for the three-band Hubbard model have also found nematic phases in certain parameter regimes [31][32][33] .…”