arXiv subjects

Robin Scholle

Publications and source records attributed to Robin Scholle.

4 recordsLinked to original sources

arXiv2026

Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model

We perform a renormalized mean-field study of the two-dimensional repulsive Hubbard model, focusing on the intricate interplay and possible coexistence of magnetic, charge, and superconducting orders. We improve on conventional mean-field theory by utilizing a renormalization group framework that captures high-energy fluctuations. This method generates effective magnetic and $d$-wave pairing interactions, and allows for an unbiased exploration of coexisting phases at weak and moderate interaction strengths. Unrestricted mean-field calculations of the effective Hamiltonian on large finite lattices are combined with analyses in the thermodynamic limit, revealing a rich phase diagram with extensive regions of coexisting orders. We find that $d$-wave superconductivity coexists with N\'eel order on the electron-doped side. On the hole-doped side, superconductivity is found to coexist with spiral or stripe magnetic orders. Within the stripe ordered region, the superconducting order parameter is spatially modulated, with a period that follows the charge modulation of the stripes. Below van Hove filling, pairing provides the primary energy gain, while the stripe order yields only a small, and hence fragile, additional energy lowering.

cond-mat.str-el↗

arXiv2024

Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene

We perform unrestricted Hartree-Fock calculations on the 2D Hubbard model on a honeycomb and bilayer honeycomb lattice at both zero and finite temperatures. Finite size real space calculations are supplemented with RPA calculations in the thermodynamic limit. Our motivation comes from high doping levels achieved in graphene and Bernal bilayer graphene by interacalation. We present phase diagrams in doping and temperature for a moderate Hubbard interaction. The magnetic states we find are classified systematically based on the dominant Fourier components of their spin patterns, their average magnetization and spin incommensurabilities. The dominant spin patterns are N\'eel order and various types of stripes. Around Van Hove filling, we resolve the competition between stripe and chiral spin density waves in the symmetry-broken regime. We also investigate the effect of an applied external displacement field on the spin patterns of BBG.

cond-mat.str-el↗

arXiv2024

Spiral to stripe transition in the two-dimensional Hubbard model

We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [Phys. Rev. B 108, 035139 (2023)] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature $T^*$ by a Landau free energy analysis. While the magnetic order for filling factors $n \geq 1$ is always of N\'eel type, for $n \leq 1$ the following sequence of magnetic states is found as a function of increasing hole-doping: N\'eel, planar circular spiral, multi-spiral, and collinear spin-charge stripe states. Multi-spiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram.

cond-mat.str-el↗

arXiv2023

Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model

We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, both at zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to Néel and circular spiral order in the thermodynamic limit. The magnetic states are classified by a systematic scheme based on the dominant Fourier components of the spin texture. On finite lattices a whole zoo of ordering patterns appears. We show that many of these states are finite size artifacts related to the limited choice of ordering wave vectors on a finite lattice. In the thermodynamic limit only three classes of states with a relatively simple structure survive: Néel, circular spiral, and stripe states. Stripes involve also charge order and can be unidirectional or bidirectional, with horizontal and/or vertical orientation. We present complete phase diagrams in the plane spanned by electron density and temperature, for a moderate Hubbard interaction and various choices of the next-nearest neighbor hopping amplitude.

cond-mat.str-el↗