arXiv:cond-mat/0101462 · Physical review. B, Condensed matter

Single hole dynamics in the t−J model on two- and three-leg ladders

Michael Brunner, Sylvain Capponi, Fakher F. Assaad, Alejandro Muramatsu

Published Apr 23, 2001• 19 citations

Abstract

The dynamics of a single hole in the $t\ensuremath{-}J$ model on two- (2LL) and three- (3LL) leg ladders is studied using a recently developed quantum Monte Carlo algorithm. For the 2LL it is shown that in addition to the most pronounced features of the spectral function, well described by the limit of strong coupling along the rungs, a clear shadow band appears in the antibonding channel. Moreover, both the bonding band and its shadow have a finite quasiparticle (QP) weight in the thermodynamic limit. For strong coupling along the rungs of the 3LL, the low-energy spectrum in the antisymmetric channel is similar to a one-dimensional chain, whereas in the two symmetric channels it resembles the 2LL. The QP weight vanishes in the antisymmetric channel, but is finite in the symmetric one.

DOI: 10.1103/physrevb.63.180511

Related papers

Single-hole dynamics in dimerized and frustrated spin chains

Christoph Jurecka, Wolfram Brenig

arXiv:cond-mat/0007447Physical review. B, Condensed matterFeb 5, 200116 citations

Single-hole dynamics in the t−J model on a square lattice

Michael Brunner, Fakher F. Assaad, Alejandro Muramatsu

arXiv:cond-mat/0002321Physical review. B, Condensed matterDec 15, 2000110 citations

Phase diagram of coupled ladders

T. F. A. Müller, Thomas Maurice Rice

arXiv:cond-mat/9802297Physical review. B, Condensed matterAug 1, 199818 citations

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

Shenxiu Liu, Hong‐Chen Jiang, Thomas Devereaux

arXiv:1606.03762Physical review. B./Physical review. BOct 28, 201611 citations

Properties of lightly dopedt-Jtwo-leg ladders

Matthias Troyer, Hirokazu Tsunetsugu, Thomas Maurice Rice

arXiv:cond-mat/9510150Physical review. B, Condensed matterJan 1, 1996173 citations

Two-hole dynamics in spin ladders

Christoph Jurecka, Wolfram Brenig

arXiv:cond-mat/0107365Jul 17, 20010 citations

arXiv:cond-mat/0101462 · Physical review. B, Condensed matter

Single hole dynamics in the t−J model on two- and three-leg ladders

Michael Brunner, Sylvain Capponi, Fakher F. Assaad, Alejandro Muramatsu

Published Apr 23, 2001• 19 citations

arXiv HTML PDF

Abstract

The dynamics of a single hole in the

t\ensuremath{-}J

model on two- (2LL) and three- (3LL) leg ladders is studied using a recently developed quantum Monte Carlo algorithm. For the 2LL it is shown that in addition to the most pronounced features of the spectral function, well described by the limit of strong coupling along the rungs, a clear shadow band appears in the antibonding channel. Moreover, both the bonding band and its shadow have a finite quasiparticle (QP) weight in the thermodynamic limit. For strong coupling along the rungs of the 3LL, the low-energy spectrum in the antisymmetric channel is similar to a one-dimensional chain, whereas in the two symmetric channels it resembles the 2LL. The QP weight vanishes in the antisymmetric channel, but is finite in the symmetric one.

DOI: 10.1103/physrevb.63.180511

Related papers

Single-hole dynamics in dimerized and frustrated spin chains

Christoph Jurecka, Wolfram Brenig

We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional ${t}_{1,2,3}$ - ${J}_{1,2,3}$ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional ${t}_{1,2,3}$-${J}_{1,2,3}$ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.

arXiv:cond-mat/0007447Physical review. B, Condensed matterFeb 5, 200116 citations

Single-hole dynamics in the t−J model on a square lattice

Michael Brunner, Fakher F. Assaad, Alejandro Muramatsu

We present quantum Monte Carlo (QMC) simulations for a single hole in a $t\ensuremath{-}J$ model from $J=0.4t$ to $J=4t$ on square lattices with up to $24\ifmmode\times\else\texttimes\fi{}24$ sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}),$ $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and the minimum of the dispersion at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For small J, both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for $J/t>1,$ only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite-size scaling of the quasiparticle weight $Z(\stackrel{\ensuremath{\rightarrow}}{k})$ that leads to a finite result in the thermodynamic limit for the considered values of $J/t.$ The spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J dependence is quantitatively described by string excitations up to $J/t=2.$ We present quantum Monte Carlo (QMC) simulations for a single hole in a $t\ensuremath{-}J$ model from $J=0.4t$ to $J=4t$ on square lattices with up to $24\ifmmode\times\else\texttimes\fi{}24$ sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}),$ $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and the minimum of the dispersion at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For small J, both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for $J/t>1,$ only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite-size scaling of the quasiparticle weight $Z(\stackrel{\ensuremath{\rightarrow}}{k})$ that leads to a finite result in the thermodynamic limit for the considered values of $J/t.$ The spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J dependence is quantitatively described by string excitations up to $J/t=2.$

arXiv:cond-mat/0002321Physical review. B, Condensed matterDec 15, 2000110 citations

Phase diagram of coupled ladders

T. F. A. Müller, Thomas Maurice Rice

The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio $J/t.$ Two known limiting cases are $n<\frac{1}{2},$ which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for $1>n>\frac{1}{2}.$ We find evidences for gapless behavior in both spin and charge channels for $J/t<0.3,$ consistent with Luttinger liquids in both bonding and antibonding bands (i.e., $C2S2).$ This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger $J/t$ shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For $J/t<0.3$ this is very weak, indicating a lack of pairing between these channels.The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio $J/t.$ Two known limiting cases are $n<\frac{1}{2},$ which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for $1>n>\frac{1}{2}.$ We find evidences for gapless behavior in both spin and charge channels for $J/t<0.3,$ consistent with Luttinger liquids in both bonding and antibonding bands (i.e., $C2S2).$ This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger $J/t$ shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For $J/t<0.3$ this is very weak, indicating a lack of pairing between these channels.

arXiv:cond-mat/9802297Physical review. B, Condensed matterAug 1, 199818 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.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:1606.03762Physical review. B./Physical review. BOct 28, 201611 citations

Properties of lightly dopedt-Jtwo-leg ladders

Matthias Troyer, Hirokazu Tsunetsugu, Thomas Maurice Rice

We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong interchain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong interchain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large J/t the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge +\ensuremath{\Vert}e\ensuremath{\Vert} and spin 1/2 and a triplet magnon mode. At half filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on two-dimensional clusters. \textcopyright{} 1996 The American Physical Society.We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong interchain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong interchain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large J/t the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge +\ensuremath{\Vert}e\ensuremath{\Vert} and spin 1/2 and a triplet magnon mode. At half filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on two-dimensional clusters. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9510150Physical review. B, Condensed matterJan 1, 1996173 citations

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.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/0107365Jul 17, 20010 citations

The dynamics of a single hole in the

t\ensuremath{-}J

{t}_{1,2,3}

{J}_{1,2,3}

model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.

We present quantum Monte Carlo (QMC) simulations for a single hole in a $t\ensuremath{-}J$ model from

J=0.4t

J=4t

on square lattices with up to $24\ifmmode\times\else\texttimes\fi{}24$ sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}),$ $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and the minimum of the dispersion at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For small J, both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for

J/t>1,

only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite-size scaling of the quasiparticle weight $Z(\stackrel{\ensuremath{\rightarrow}}{k})$ that leads to a finite result in the thermodynamic limit for the considered values of

J/t.

The spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J dependence is quantitatively described by string excitations up to

J/t=2.

J/t.

Two known limiting cases are

n<\frac{1}{2},

which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for

1>n>\frac{1}{2}.

We find evidences for gapless behavior in both spin and charge channels for

J/t<0.3,

consistent with Luttinger liquids in both bonding and antibonding bands (i.e.,

C2S2).

This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger

J/t

shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For

J/t<0.3

this is very weak, indicating a lack of pairing between these channels.

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.