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:cond-mat/0104122 · Physical review. B, Condensed matter

Quantum Monte Carlo simulations of the t−Jz model with stripes on the square lattice

José A. Riera

Published Aug 23, 2001• 21 citations
arXivHTMLPDF

Abstract

Finite temperature quantum Monte Carlo simulations are performed on the anisotropic $t\ensuremath{-}J$ model and in particular on its Ising limit. Straight site-centered stripes are imposed by an on-site potential representing external mechanisms of stripe formation. In this model, we show that, even though charge inhomogeneity exists at a high temperature, the antiphase ordering of the spin domains between stripes occurs at a much lower temperature. The magnetic correlations at this spin ordering crossover are analyzed. The stripes show metallicity, with absence of hole attraction. Comparison between this model and others that have been proposed to explain or describe stripes, as well as possible relations with experimental features on underdoped cuprates are discussed.

DOI
10.1103/physrevb.64.104520

Related papers

Charge and spin ordering and charge transport properties in a two-dimensional inhomogeneous t−J model

José A. Riera

We study a two-dimensional $t\ensuremath{-}J$ model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential ${e}_{s},$ by using diagonalization in a restricted Hilbert space and finite temperature quantum Monte Carlo techniques. Both site- and bond-centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as ${e}_{s}\ensuremath{\rightarrow}0.$ Moreover, we show that the antiphase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic behavior of the stripes with no signs of hole attraction. Kinetic energies and current susceptibilities are computed and indications of charge localization are discussed. The study of the doping dependence in the range $0.083<~x<~0.167$ suggests that these features are characteristic of the whole underdoped region.

arXiv:cond-mat/0108446•Physical review. B, Condensed matter•Jan 22, 2002•4 citations

Inhomogeneous state of the extended t - J model on a square lattice: A variational Monte Carlo and Gutzwiller approximation study

Chung-Pin Chou, Ting-Kuo Lee

We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the $t$-$J$ model. It leads to the stripe patterns we have found numerically in a generalized $t$-$J$-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust $d$-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.

Physical Review B•Mar 14, 2012•11 citations

Effects of domain walls on hole motion in the two-dimensional anisotropic t−J model at finite temperature

José A. Riera

The $t\ensuremath{-}J$ model on the square lattice, close to the $t\ensuremath{-}{J}_{z}$ limit, is studied by quantum Monte Carlo techniques at finite temperature and in the underdoped regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify the antiferromagnetic domains on each Trotter slice. The results show that the model at high enough temperature presents finite antiferromagnetic (AF) domains, which collapse at lower temperatures into a single ordered AF state. While there are domains, holes would tend to preferentially move along the domain walls. In this case, there are indications of hole pairing starting at a relatively high temperature. At lower temperatures, when the whole system becomes essentially fully AF ordered, at least in finite clusters, holes would likely tend to move within phase separated regions. The crossover between both states moves down in temperature as doping increases and/or as the off-diagonal exchange increases. The possibility of hole motion along AF domain walls at zero temperature in the fully isotropic $t\ensuremath{-}J$ is discussed.

arXiv:cond-mat/0304204•Physical review. B, Condensed matter•Aug 26, 2003•0 citations

Nature of the inhomogeneous state of the extended t-J model on a square lattice

Chung-Pin Chou, Ting-Kuo Lee

We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density and pair field, of the mean-field ground state of the t-J model. It leads to the stripe patterns we have found numerically in a generalized t-J-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust d-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the "in-phase" magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.

arXiv:1112.5787•Physical Review B•Dec 25, 2011•0 citations

Stripes in the extended $t-t^\prime$ Hubbard model: A Variational Monte Carlo analysis

Vito Marino, Federico Becca, Luca F. Tocchio

By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping \delta=1/8 δ = 1 / 8 , with both nearest- ( t t ) and next-nearest-neighbor hopping ( t^\prime t ′ ). Stripes with different wavelengths \lambda λ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction U/t U / t . The general trend is that \lambda λ increases going from negative to positive values of t^\prime/t t ′ / t and decreases by increasing U/t U / t . In particular, the \lambda=8 λ = 8 stripe obtained for t^\prime=0 t ′ = 0 and U/t=8 U / t = 8 [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 21 (2019)] shrinks to \lambda=6 λ = 6 for U/t\gtrsim 10 U / t ≳ 10 . For t^\prime/t<0 t ′ / t < 0 , the stripe with \lambda=5 λ = 5 </

arXiv:2111.04623•SciPost Physics•Jun 1, 2022•13 citations

Formation of individual stripes in a mixed-dimensional cold-atom Fermi–Hubbard system

Dominik Bourgund, Thomas Chalopin, Petar Bojović +8 more

Abstract The relation between d -wave superconductivity and stripes is fundamental to the understanding of ordered phases in high-temperature cuprate superconductors 1–6 . These phases can be strongly influenced by anisotropic couplings, leading to higher critical temperatures, as emphasized by the recent discovery of superconductivity in nickelates 7–10 . Quantum simulators with ultracold atoms provide a versatile platform to engineer such couplings and to observe emergent structures in real space with single-particle resolution. Here we show, to our knowledge, the first signatures of individual stripes in a cold-atom Fermi–Hubbard quantum simulator using mixed-dimensional (mixD) settings. Increasing the energy scale of hole–hole attraction to the spin exchange energy, we access the interesting crossover temperature regime in which stripes begin to form 11 . We observe extended, attractive correlations between hole dopants and find an increased probability of forming larger structures akin to individual stripes. In the spin sector, we study correlation functions up to the third order and find results consistent with stripe formation. These observations are interpreted as a precursor to the stripe phase, which is characterized by interleaved charge and spin density wave ordering with fluctuating lines of dopants separating domains of opposite antiferromagnetic order 12–14 .

arXiv:2312.14156•Nature•Jan 1, 2025•23 citations
Finite temperature quantum Monte Carlo simulations are performed on the anisotropic t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model and in particular on its Ising limit. Straight site-centered stripes are imposed by an on-site potential representing external mechanisms of stripe formation. In this model, we show that, even though charge inhomogeneity exists at a high temperature, the antiphase ordering of the spin domains between stripes occurs at a much lower temperature. The magnetic correlations at this spin ordering crossover are analyzed. The stripes show metallicity, with absence of hole attraction. Comparison between this model and others that have been proposed to explain or describe stripes, as well as possible relations with experimental features on underdoped cuprates are discussed.
We study a two-dimensional $t\ensuremath{-}J$ model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential es,{e}_{s},es​, by using diagonalization in a restricted Hilbert space and finite temperature quantum Monte Carlo techniques. Both site- and bond-centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as ${e}_{s}\ensuremath{\rightarrow}0.$ Moreover, we show that the antiphase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic behavior of the stripes with no signs of hole attraction. Kinetic energies and current susceptibilities are computed and indications of charge localization are discussed. The study of the doping dependence in the range 0.083< x< 0.1670.083<~x<~0.1670.083< x< 0.167 suggests that these features are characteristic of the whole underdoped region.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the ttt-JJJ model. It leads to the stripe patterns we have found numerically in a generalized ttt-JJJ-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust ddd-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.
The $t\ensuremath{-}J$ model on the square lattice, close to the $t\ensuremath{-}{J}_{z}$ limit, is studied by quantum Monte Carlo techniques at finite temperature and in the underdoped regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify the antiferromagnetic domains on each Trotter slice. The results show that the model at high enough temperature presents finite antiferromagnetic (AF) domains, which collapse at lower temperatures into a single ordered AF state. While there are domains, holes would tend to preferentially move along the domain walls. In this case, there are indications of hole pairing starting at a relatively high temperature. At lower temperatures, when the whole system becomes essentially fully AF ordered, at least in finite clusters, holes would likely tend to move within phase separated regions. The crossover between both states moves down in temperature as doping increases and/or as the off-diagonal exchange increases. The possibility of hole motion along AF domain walls at zero temperature in the fully isotropic $t\ensuremath{-}J$ is discussed.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density and pair field, of the mean-field ground state of the t-J model. It leads to the stripe patterns we have found numerically in a generalized t-J-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust d-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the "in-phase" magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.
Stripes in the extended t−t′t-t^\primet−t′ Hubbard model: A Variational Monte Carlo analysis
By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping \delta=1/8 δ = 1 / 8 , with both nearest- ( t t ) and next-nearest-neighbor hopping ( t^\prime t ′ ). Stripes with different wavelengths \lambda λ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction U/t U / t . The general trend is that \lambda λ increases going from negative to positive values of t^\prime/t t ′ / t and decreases by increasing U/t U / t . In particular, the \lambda=8 λ = 8 stripe obtained for t^\prime=0 t ′ = 0 and U/t=8 U / t = 8 [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 21 (2019)] shrinks to \lambda=6 λ = 6 for U/t\gtrsim 10 U / t ≳ 10 . For t^\prime/t<0 t ′ / t < 0 , the stripe with \lambda=5 λ = 5 </
Abstract The relation between d -wave superconductivity and stripes is fundamental to the understanding of ordered phases in high-temperature cuprate superconductors 1–6 . These phases can be strongly influenced by anisotropic couplings, leading to higher critical temperatures, as emphasized by the recent discovery of superconductivity in nickelates 7–10 . Quantum simulators with ultracold atoms provide a versatile platform to engineer such couplings and to observe emergent structures in real space with single-particle resolution. Here we show, to our knowledge, the first signatures of individual stripes in a cold-atom Fermi–Hubbard quantum simulator using mixed-dimensional (mixD) settings. Increasing the energy scale of hole–hole attraction to the spin exchange energy, we access the interesting crossover temperature regime in which stripes begin to form 11 . We observe extended, attractive correlations between hole dopants and find an increased probability of forming larger structures akin to individual stripes. In the spin sector, we study correlation functions up to the third order and find results consistent with stripe formation. These observations are interpreted as a precursor to the stripe phase, which is characterized by interleaved charge and spin density wave ordering with fluctuating lines of dopants separating domains of opposite antiferromagnetic order 12–14 .