Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2509.24439 · Physical review. B./Physical review. B

Spin stripes in the Hubbard model: A combined dynamical mean-field theory and Bethe-Salpeter analysis

Ruslan Mushkaev, Francesco Petocchi, Shintaro Hoshino, Philipp Werner

Published Dec 9, 2025• 1 citation
arXivHTMLPDF

Abstract

The Hubbard model is known to accommodate various electronic orders, including stripes, which are important for understanding the physics of cuprates. We study spin-stripe order in the square lattice Hubbard model as a function of doping and temperature, by solving the Bethe-Salpeter equation with the local vertex from dynamical mean field theory (DMFT), both inside and outside the antiferromagnetic phase. We find broad regions of horizontal/vertical spin stripes at low temperatures for the model with and without next-nearest neighbor hopping. Their wavelength depends on hole doping in a nonlinear fashion, and is highly sensitive to the ratio of nearest and next-nearest neighbor hoppings.

DOI
10.1103/pqgq-qf7j

Related papers

Stripe order from the perspective of the Hubbard model

Edwin W. Huang, Christian B. Mendl, Hong‐Chen Jiang +2 more

Abstract A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.

arXiv:1709.02398•npj Quantum Materials•Apr 13, 2018•149 citations

Spiral to stripe transition in the two-dimensional Hubbard model

Robin Scholle, Walter Metzner, Demetrio Vilardi +1 more

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 [] 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 ≥ 1 is always of Néel type, for n ≤ 1 the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral 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. Published by the American Physical Society 2024

arXiv:2403.09862•Physical review. B./Physical review. B•Jun 27, 2024•12 citations

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

Robin Scholle, Pietro M. Bonetti, Demetrio Vilardi +1 more

We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, at both zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to N\'eel 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: N\'eel, 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.

arXiv:2303.15358•Physical review. B./Physical review. B•Jul 19, 2023•33 citations

Coexistence of superconductivity with partially filled stripes in the Hubbard model

Hao Xu, Chia-Min Chung, Mingpu Qin +3 more

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

arXiv:2303.08376•Science•May 9, 2024•144 citations

Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram

Hao Xu, Hao Shi, Ettore Vitali +2 more

We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near $1/8$ doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about $1/5$ doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.

arXiv:2112.02187•Physical Review Research•Mar 28, 2022•74 citations

Dynamical Mean-Field Theory of Stripe Ordering

Alexander I. Lichtenstein, Marcus Fleck, Andrzej M. Oleś +1 more

Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooks•Mar 29, 2006•0 citations
The Hubbard model is known to accommodate various electronic orders, including stripes, which are important for understanding the physics of cuprates. We study spin-stripe order in the square lattice Hubbard model as a function of doping and temperature, by solving the Bethe-Salpeter equation with the local vertex from dynamical mean field theory (DMFT), both inside and outside the antiferromagnetic phase. We find broad regions of horizontal/vertical spin stripes at low temperatures for the model with and without next-nearest neighbor hopping. Their wavelength depends on hole doping in a nonlinear fashion, and is highly sensitive to the ratio of nearest and next-nearest neighbor hoppings.
Abstract A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.
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 [] 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 ≥ 1 is always of Néel type, for n ≤ 1 the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral 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. Published by the American Physical Society 2024
We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, at both zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to N\'eel 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: N\'eel, 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.
The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.