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

AIP conference proceedings

Bound states of holes in distorted spin ladder

Akiomi Mishima

Published Jan 1, 2001• 0 citations
Publisher

Abstract

The effects of the lattice distortions along the rung on the bound states of two holes doped away from half-filling in terms of electrons have been studied in the two-leg-spin ladders. As the electron-lattice interaction increases, the binding energy of two holes with negative value increases. Two holes along the rung form bound states with the spin singlet. It turns out that the electron-lattice interaction along the rung plays an important role in the bound states of two holes in the two-leg-spin ladders.

DOI
10.1063/1.1363079

Related papers

Two-hole dynamics in spin ladders

Christoph Jurecka, Wolfram Brenig

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.

arXiv:cond-mat/0107365•Jul 17, 2001•0 citations

Quantum Monte Carlo Study of the Hubbard Ladder

Yasuko Munehisa

We present quantum Monte Carlo results for the Hubbard model on a ladder using the re-structuring method which employ eigenstates of two-site system on a rung to construct a complete set. From technical reasons we concentrate on the case in which the hopping along the leg is much less than the hopping on the rung. We observe the ground state of the half-filled system is made of singlet-like states described in this paper and its first excited state contains one triplet rung. When the system is lightly doped states composed of an electron and a hole appear on some rungs. We find very few hole-pairing on the rung upon doping up to the quarter-filled case.

arXiv:cond-mat/9510039•Oct 8, 1995•0 citations

Bosonic model of hole pairs

Thomas Siller, Matthias Troyer, Thomas Maurice Rice +1 more

We numerically investigate a bosonic representation for hole pairs on a two-leg $t\ensuremath{-}J$ ladder where hard core bosons on a chain represent the hole pairs on the ladder. The interaction between hole pairs is obtained by fitting the density profile obtained with the effective model to the one obtained with the $t\ensuremath{-}J$ model, taking into account the inner structure of the hole pair given by the hole-hole correlation function. For these interactions we calculate the Luttinger liquid parameter, which takes the universal value ${K}_{\ensuremath{\rho}}=1$ as half filling is approached, for values of the rung exchange ${J}^{\ensuremath{'}}$ between strong coupling and the isotropic case. The long distance behavior of the hole-hole correlation function is also investigated. Starting from large ${J}^{\ensuremath{'}},$ the correlation length first increases as expected but diminishes significantly as ${J}^{\ensuremath{'}}$ is reduced and bound holes sit mainly on adjacent rungs. As the isotropic case is approached, the correlation length increases again. This effect is related to the different kind of bonds in the region between the two holes of a hole pair when they move apart.

arXiv:cond-mat/0006080•Physical review. B, Condensed matter•Apr 24, 2001•30 citations

Nature of a single doped hole in two-leg Hubbard and t−J ladders

Shenxiu Liu, Hong‐Chen Jiang, Thomas Devereaux

In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.

arXiv:1606.03762•Physical review. B./Physical review. B•Oct 28, 2016•11 citations

Differences between hole and electron doping of a two-leg CuO ladder

Satoshi Nishimoto, Eric Jeckelmann, Douglas J. Scalapino

Here we report results of a density-matrix-renormalization-group calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This model allows us to study the effects of hole and electron doping on a system that is a charge-transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes and with electrons.

arXiv:cond-mat/0208189•Physical review. B, Condensed matter•Dec 20, 2002•31 citations

Spin and charge modulations in a single-hole-doped Hubbard ladder: Verification with optical lattice experiments

Zheng Zhu, Zheng-Yu Weng, Tin-Lun Ho

We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or ``phase strings'') left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and interchain hopping. Remarkably, all these properties persist down to ladders as short as $\ensuremath{\sim}10$ sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.

arXiv:1510.00035•Physical Review A•Mar 7, 2016•8 citations
The effects of the lattice distortions along the rung on the bound states of two holes doped away from half-filling in terms of electrons have been studied in the two-leg-spin ladders. As the electron-lattice interaction increases, the binding energy of two holes with negative value increases. Two holes along the rung form bound states with the spin singlet. It turns out that the electron-lattice interaction along the rung plays an important role in the bound states of two holes in the two-leg-spin ladders.
We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding t1,2−J1,2t_{1,2}-J_{1,2}t1,2​−J1,2​ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.
We present quantum Monte Carlo results for the Hubbard model on a ladder using the re-structuring method which employ eigenstates of two-site system on a rung to construct a complete set. From technical reasons we concentrate on the case in which the hopping along the leg is much less than the hopping on the rung. We observe the ground state of the half-filled system is made of singlet-like states described in this paper and its first excited state contains one triplet rung. When the system is lightly doped states composed of an electron and a hole appear on some rungs. We find very few hole-pairing on the rung upon doping up to the quarter-filled case.
We numerically investigate a bosonic representation for hole pairs on a two-leg $t\ensuremath{-}J$ ladder where hard core bosons on a chain represent the hole pairs on the ladder. The interaction between hole pairs is obtained by fitting the density profile obtained with the effective model to the one obtained with the $t\ensuremath{-}J$ model, taking into account the inner structure of the hole pair given by the hole-hole correlation function. For these interactions we calculate the Luttinger liquid parameter, which takes the universal value ${K}_{\ensuremath{\rho}}=1$ as half filling is approached, for values of the rung exchange ${J}^{\ensuremath{'}}$ between strong coupling and the isotropic case. The long distance behavior of the hole-hole correlation function is also investigated. Starting from large ${J}^{\ensuremath{'}},$ the correlation length first increases as expected but diminishes significantly as ${J}^{\ensuremath{'}}$ is reduced and bound holes sit mainly on adjacent rungs. As the isotropic case is approached, the correlation length increases again. This effect is related to the different kind of bonds in the region between the two holes of a hole pair when they move apart.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
Here we report results of a density-matrix-renormalization-group calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This model allows us to study the effects of hole and electron doping on a system that is a charge-transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes and with electrons.
We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or ``phase strings'') left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and interchain hopping. Remarkably, all these properties persist down to ladders as short as $\ensuremath{\sim}10$ sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.