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/0011098 · Physical review. B, Condensed matter

Density matrix renormalization group analysis of the Nagaoka polaron in the two-dimensional t−J model

Steven R. White, Ian K. Affleck

Published Jun 19, 2001• 68 citations
arXivHTMLPDF

Abstract

It is widely believed that a single hole in the two- (or three-)dimensional $t\ensuremath{-}J$ model, for sufficiently small exchange coupling J, creates a ferromagnetic bubble around itself, a finite J remnant of the ferromagnetic ground state at $J=0$ (the infinite U Hubbard model), first established by Nagaoka [Phys. Rev. 147, 392 (1966)]. We investigate this phenomenon in two dimensions using the density matrix renormalization group, for system sizes up to $9\ifmmode\times\else\texttimes\fi{}9.$ We find that the polaron forms for $J/t<0.02\ensuremath{-}0.03.$ Although finite-size effects appear large, our data seems consistent with the expected ${1.1(J/t)}^{\ensuremath{-}1/4}$ variation of polarion radius. We also test the Brinkman-Rice model of nonretracing paths in a N\'eel background, showing that it is quite accurate, at larger J. Results are also presented in the case where the Heisenberg interaction is dropped (the $t\ensuremath{-}{J}^{z}$ model). Finally we discuss a ``dressed polaron'' picture in which the hole propagates freely inside a finite region but makes only self-retracing excursions outside this region.

DOI
10.1103/physrevb.64.024411

Related papers

Effective approach to the Nagaoka regime of the two-dimensional t - J model

Maciej M. Maśka, Marcin Mierzejewski, E. A. Kochetov +3 more

We argue that the $t$-$J$ model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for $J/t\ensuremath{\ll}1$. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard $t$-$J$ or $t$-${J}_{z}$ models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking advantage of this fact, we study the low doping regime of the $t$-$J$ model for $J/t\ensuremath{\ll}1$ and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes $\ensuremath{\delta}\ensuremath{\le}{\ensuremath{\delta}}_{t}\ensuremath{\simeq}0.44\sqrt{J/t}$. Analytical calculations show that ${\ensuremath{\delta}}_{t}=\sqrt{J/2\ensuremath{\pi}t}$.

arXiv:1204.3824•Physical Review B•Jun 14, 2012•16 citations

Nagaoka Ferromagnetism in the Two-Dimensional Infinite- U Hubbard Model

Federico Becca, Sandro Sorella

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.

arXiv:cond-mat/0102249•Physical Review Letters•Apr 9, 2001•58 citations

Ferromagnetic domains in the large- U Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo study

Su-Jun Yun, Werner Dobrautz, Hongjun Luo +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.

Physical review. B./Physical review. B•Feb 7, 2023•8 citations

Ferromagnetic domains in the large-$U$ Hubbard model with a few holes: an FCIQMC study

Yun, Sujun, Werner Dobrautz, Luo Hongjun +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.

arXiv:2210.12049•Oct 21, 2022•1 citation

Sub-dimensional magnetic polarons in the one-hole doped SU(3) $t$-$J$ model

Henning Schlömer, Fabian Grusdt, Ulrich Schollwöck +2 more

The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t$-$J$ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.

arXiv:2312.14137•Dec 21, 2023•1 citation

Dynamical formation of a magnetic polaron in a two-dimensional quantum antiferromagnet

Annabelle Bohrdt, F Grusdt, M Knap

Abstract Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t–J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number z ̃ = 4 . Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.

arXiv:1907.08214•New Journal of Physics•Dec 1, 2020•39 citations
It is widely believed that a single hole in the two- (or three-)dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, for sufficiently small exchange coupling J, creates a ferromagnetic bubble around itself, a finite J remnant of the ferromagnetic ground state at J=0J=0J=0 (the infinite U Hubbard model), first established by Nagaoka [Phys. Rev. 147, 392 (1966)]. We investigate this phenomenon in two dimensions using the density matrix renormalization group, for system sizes up to 9\ifmmode×\else\texttimes\fi9.9\ifmmode\times\else\texttimes\fi{}9.9\ifmmode×\else\texttimes\fi9. We find that the polaron forms for J/t<0.02\ensuremath−0.03.J/t<0.02\ensuremath{-}0.03.J/t<0.02\ensuremath−0.03. Although finite-size effects appear large, our data seems consistent with the expected 1.1(J/t)\ensuremath−1/4{1.1(J/t)}^{\ensuremath{-}1/4}1.1(J/t)\ensuremath−1/4 variation of polarion radius. We also test the Brinkman-Rice model of nonretracing paths in a N'eel background, showing that it is quite accurate, at larger J. Results are also presented in the case where the Heisenberg interaction is dropped (the t\ensuremath−Jzt\ensuremath{-}{J}^{z}t\ensuremath−Jz model). Finally we discuss a ``dressed polaron'' picture in which the hole propagates freely inside a finite region but makes only self-retracing excursions outside this region.
We argue that the ttt-JJJ model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for $J/t\ensuremath{\ll}1$. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard ttt-JJJ or ttt-Jz{J}_{z}Jz​ models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking advantage of this fact, we study the low doping regime of the ttt-JJJ model for $J/t\ensuremath{\ll}1$ and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes $\ensuremath{\delta}\ensuremath{\le}{\ensuremath{\delta}}_{t}\ensuremath{\simeq}0.44\sqrt{J/t}$. Analytical calculations show that ${\ensuremath{\delta}}_{t}=\sqrt{J/2\ensuremath{\pi}t}$.
We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
Ferromagnetic domains in the large-UUU Hubbard model with a few holes: an FCIQMC study
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.
Sub-dimensional magnetic polarons in the one-hole doped SU(3) ttt-JJJ model
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) ttt-JJJ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.
Abstract Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t–J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number z ̃ = 4 . Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.