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:2307.09500 · Physical Review Research

Exact hole-induced S U ( N ) flavor singlets in certain U = ∞ S U ( N ) Hubbard models

Kyung-Su Kim, Hosho Katsura

Published Mar 20, 2024• 4 citations
arXivHTMLPDF

Abstract

We prove that the motion of a single hole induces S U ( N ) flavor singlets in the U = ∞ S U ( N ) (Fermi) Hubbard model on a Husimi-like tree graph. The result is generalized to certain t − J models with singlet hopping terms typically neglected in the literature. This is an S U ( N ) generalization of the “counter-Nagaoka theorem” introduced in []. Our results suggest the existence of resonating flavor singlet (RFS)-like polarons in the t − J models on a more realistic nonbipartite lattice. Such RFS polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013307

Related papers

Exact hole-induced resonating-valence-bond ground state in certain U = ∞ Hubbard models

Kyung-Su Kim

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the $U=\ensuremath{\infty}$ Hubbard model on a triangular cactus---a treelike variant of a kagome lattice. The result can be easily generalized to $t\ensuremath{-}J$ models with antiferromagnetic interactions $J\ensuremath{\ge}0$ on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice.

arXiv:2207.09498•Physical review. B./Physical review. B•Apr 3, 2023•10 citations

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

Subdimensional 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 $\mathrm{SU}(N)$ spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of $\mathrm{SU}(2)$ spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t\text{\ensuremath{-}}J$ 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 $\mathrm{SU}(N)$ 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 $\mathrm{SU}(N)$ Fermi-Hubbard models on various geometries.

Physical review. B./Physical review. B•Sep 16, 2024•9 citations

Motion of a single hole in a resonating-valence-bond background: Some exact results

Indrani Bose

An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the t-J Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction J\ensuremath{\ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is also highlighted.

Physical review. B, Condensed matter•Jun 1, 1991•5 citations

Hole motion in thet-Jand Hubbard models: Effect of a next-nearest-neighbor hopping

Eduardo R. Gagliano, Silvia Bacci, Elbio R. Dagotto

Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.

Physical review. B, Condensed matter•Oct 1, 1990•30 citations

A pure Hubbard model with demonstrable pairing adjacent to the Mott-insulating phase

James Champion, M W Long

Abstract. We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intrapair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole-motion in the CuO2 planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone. Submitted to: J. Phys. A: Math. Gen. 1.

•Jan 1, 2003•1 citation
We prove that the motion of a single hole induces S U ( N ) flavor singlets in the U = ∞ S U ( N ) (Fermi) Hubbard model on a Husimi-like tree graph. The result is generalized to certain t − J models with singlet hopping terms typically neglected in the literature. This is an S U ( N ) generalization of the “counter-Nagaoka theorem” introduced in []. Our results suggest the existence of resonating flavor singlet (RFS)-like polarons in the t − J models on a more realistic nonbipartite lattice. Such RFS polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter. Published by the American Physical Society 2024
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.
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)\mathrm{SU}(N)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)\mathrm{SU}(2)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) $t\text{\ensuremath{-}}J$ 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)\mathrm{SU}(N)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)\mathrm{SU}(N)SU(N) Fermi-Hubbard models on various geometries.
An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the t-J Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction J\ensuremath{\ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​ is also highlighted.
Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.
Abstract. We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intrapair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole-motion in the CuO2 planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone. Submitted to: J. Phys. A: Math. Gen. 1.