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:1701.03623

Possibility of hole confinement in the weak coupling regime of one dimensional ising antiferromagnet and the emergence of spin-charge separation in the bulk limit

S. Ehika, Robinson O. Okanigbuan, J. O. A. Idiodi

Published Jan 13, 2017• 0 citations
arXivHTMLPDF

Abstract

The energy of one hole in one dimensional Ising antiferromagnet is calculated using exact diagonalization (ED) method on finite systems with number of sites N ranging from 4 to 50. This study gives a power-law description for the hole energy in the weak coupling region (0.001 less than or equal to Jz/t and Jz/t less than or equal to 0.1).This power-law description can otherwise be understood as a weak string-like energy that tends to compromise the motion of the hole by confining it to its birth site. However, for large N, the hole is found to escape from this confinement and hence propagates as a free particle in agreement with theoretical results in the bulk limit and experimental observations from angle resolved photoemission spectroscopy (ARPES) of spin-charge separation. In the strong coupling regime (Jz/t greater than 1), the energy of the hole is found to be independent of the system size. Accordingly, the velocities corresponding to charge and spin degrees of freedom in this regime become comparable. Under this situation, the hole may be treated as a localized particle.

DOI
10.48550/arxiv.1701.03623

Related papers

Single hole in a quantum antiferromagnet: Finite-size-scaling approach

Didier Poilblanc, Heinz J. Schulz, Timothy A. L. Ziman

Exact diagonalizations of small clusters up to 26 sites are used to extrapolate the ground-state energy of a single hole in the N\'eel state of the t-${\mathit{J}}_{\mathit{z}}$ model or in the quantum antiferromagnetic (t-J model). A surprisingly rapid convergence with system size is observed for a wide range of parameters and for the largest clusters considered. In the Ising limit the energy dependence with ${\mathit{J}}_{\mathit{z}}$ is remarkably close to a ${\mathit{J}}_{\mathit{z}}^{2/3}$ law for intermediate coupling in agreement with Brinkman-Rice type of calculations. Nevertheless a small but significant bandwidth indicates that the hole can propagate coherently in this limit. Clearly the polaronic behavior \ensuremath{\sim}${\mathit{J}}_{\mathit{z}}^{1/2}$, for very small ${\mathit{J}}_{\mathit{z}}$, is out of the range of the method. When quantum fluctuations are introduced (isotropic case) the ground-state energy behavior still remains close to that of the Ising limit although an overall increase of the energy by a factor 0.3t is observed. This suggests that the ``string scenario'' might have some relevance there.

Physical review. B, Condensed matter•Sep 1, 1992•35 citations

Spin-hole polaron of thet- Jz model

Ted Barnes, Elbio R. Dagotto, Adriana Moreo +1 more

We present analytic and numerical results for the ground state of a dynamical hole in a quantum Ising antiferromagnet (the t-${J}_{z}$ model) on a two-dimensional square lattice. We find that the ground state has a localized region of reduced N\'eel order associated with the hole, with an energy that is well described by ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{h}}$/t\ensuremath{\approxeq}-3.63+2.93(${\mathit{J}}_{\mathit{z}}$/t${)}^{23}$ for 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\lesssim}${\mathit{J}}_{\mathit{z}}$/t\ensuremath{\lesssim}1. This resolves a disagreement in the literature regarding the coefficient of (${J}_{z}$/t${)}^{2/3}$. A simple string picture gives a reasonable description of the extent of the ground-state polaron in this intermediate-coupling regime. Disruption of long-range antiferromagnetic order in the bulk limit is estimated to occur at ${J}_{z}$/t\ensuremath{\approxeq}0.3 for a hole-doping fraction of x=(1/16.

Physical review. B, Condensed matter•Dec 1, 1989•33 citations

Strongly correlated electronic systems with one hole: Dynamical properties

Elbio R. Dagotto, Robert Joynt, Adriana Moreo +2 more

The spectral functions of one hole in the t-J and one-band Hubbard models are calculated using exact diagonalization techniques on small lattices. Results for the t-${\mathit{J}}_{\mathit{z}}$ model are also presented. For the t-J model we found that there is a quasiparticle at the bottom of the hole spectrum with an energy well approximated by ${\mathit{E}}_{\mathit{h}}$=-3.17+2.83${\mathit{J}}^{0.73}$ (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The rest of the spectrum is not incoherent: We identified at least two other peaks following a similar power-law behavior with J. We speculate that the J dependence of the results can be explained by a model where the hole is trapped in a confining potential as in the Ising limit. The bandwidth of the hole is linear in J in the region 0.1\ensuremath{\le}J\ensuremath{\le}0.4 although a power-law behavior is not excluded. The spectral weight of the quasiparticle grows like ${\mathit{J}}^{0.5}$ in the same region. We present new analytical results in the large J/t limit to understand the motion of the hole: In perturbation theory it can be shown that the momentum of the hole at large J/t is k=(\ensuremath{\pi},\ensuremath{\pi}) changing to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) at intermediate J/t in agreement with numerical and spin-waves results. We show analytically and numerically that the bandwidth of the quasiparticle is of order t in the large J/t limit. This result corresponds to a spin-liquid state. The one-hole spectral function of the Hubbard model is obtained for lattices with 8 and 10 sites. A quasiparticle is also observed in this case. The bandwidth and the relation with the t-J model are discussed and a comparison with recent Monte Carlo results is made. We also review and extend previous results for the ground-state properties of the t-J model.

Physical review. B, Condensed matter•May 1, 1990•315 citations

Spin-charge separation in the single-hole-doped Mott antiferromagnet

Zheng-Yu Weng, V. N. Muthukumar, D. N. Sheng +1 more

The motion of a single hole in a Mott antiferromagnet is investigated based on the $t\ensuremath{-}J$ model. An exact expression of the energy spectrum is obtained, in which the irreparable phase string effect [Phys. Rev. Lett. 77, 5102 (1996)] is explicitly present. By identifying the phase string effect with spin backflow, we point out that spin-charge separation must exist in such a system: the doped hole has to decay into a neutral spinon and a spinless holon, together with the phase string. We show that while the spinon remains coherent, the holon motion is deterred by the phase string, resulting in its localization in space. We calculate the electron spectral function which explains the line shape of the spectral function as well as the ``quasiparticle'' spectrum observed in angle-resolved photoemission experiments. Other analytic and numerical approaches are discussed based on the present framework.

arXiv:cond-mat/0008346•Physical review. B, Condensed matter•Jan 16, 2001•28 citations

Hole dynamics in the two-dimensional strong-coupling Hubbard Hamiltonian

Efthimios Kaxiras, Efstratios Manousakis

The effective Hamiltonian, obtained from the Hubbard model in the strong-coupling limit, is diagonalized exactly for a periodic two-dimensional square lattice of ten sites. We obtain the ground state of the system for any filling of the lattice and the $K$-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio $\frac{t}{U}$, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing $\frac{t}{U}$, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of $\frac{t}{U}$ exists for which pairing of the holes may be possible.

Physical review. B, Condensed matter•Jul 1, 1988•66 citations

A single hole in a quantum antiferromagnet: selfconsistent Green’s function approach

Gerardo Martı́nez, Peter Horsch

We solved numerically the integral equation for the selfenergy which describes the motion of a single hole in a two-dimensional quantum antiferromagnet (AF) within the selfconsistent Born approximation. This formulation stresses the similarity of the AF-spin polaron with the standard polaron problem. We confine our calculation to finite cluster geometries and compare with results from previous exact diagonalization studies. The spectral function is characterized by a narrow quasiparticle (qp) peak at the low energy side of the spectra, which appears to be well separated from the incoherent band part for large enough J values. For small J we find a reduced width of ~7t for the incoherent band. The bottom of the coherent qp band always occurs at (±π/2, ±π/2). Its bandwidth initially increases with J until J≃t and then decreases as 2t2/J. A complete characterization of our solution is given, including the dispersion relation and effective masses of this quasiparticle. The comparison with exact diagonalization studies for a 4×4 cluster is remarkably good. From our results we see that a lattice of 16×16 sites describes adequately the thermodynamic limit. We conclude that the simple Born approximation is a valuable scheme to characterize the dynamics of one hole in the t-J model. both in the perturbative and the strong coupling regimes.

International Journal of Modern Physics B•Jan 1, 1991•12 citations
The energy of one hole in one dimensional Ising antiferromagnet is calculated using exact diagonalization (ED) method on finite systems with number of sites N ranging from 4 to 50. This study gives a power-law description for the hole energy in the weak coupling region (0.001 less than or equal to Jz/t and Jz/t less than or equal to 0.1).This power-law description can otherwise be understood as a weak string-like energy that tends to compromise the motion of the hole by confining it to its birth site. However, for large N, the hole is found to escape from this confinement and hence propagates as a free particle in agreement with theoretical results in the bulk limit and experimental observations from angle resolved photoemission spectroscopy (ARPES) of spin-charge separation. In the strong coupling regime (Jz/t greater than 1), the energy of the hole is found to be independent of the system size. Accordingly, the velocities corresponding to charge and spin degrees of freedom in this regime become comparable. Under this situation, the hole may be treated as a localized particle.
Exact diagonalizations of small clusters up to 26 sites are used to extrapolate the ground-state energy of a single hole in the N\'eel state of the t-Jz{\mathit{J}}_{\mathit{z}}Jz​ model or in the quantum antiferromagnetic (t-J model). A surprisingly rapid convergence with system size is observed for a wide range of parameters and for the largest clusters considered. In the Ising limit the energy dependence with Jz{\mathit{J}}_{\mathit{z}}Jz​ is remarkably close to a Jz2/3{\mathit{J}}_{\mathit{z}}^{2/3}Jz2/3​ law for intermediate coupling in agreement with Brinkman-Rice type of calculations. Nevertheless a small but significant bandwidth indicates that the hole can propagate coherently in this limit. Clearly the polaronic behavior \ensuremath{\sim}Jz1/2{\mathit{J}}_{\mathit{z}}^{1/2}Jz1/2​, for very small Jz{\mathit{J}}_{\mathit{z}}Jz​, is out of the range of the method. When quantum fluctuations are introduced (isotropic case) the ground-state energy behavior still remains close to that of the Ising limit although an overall increase of the energy by a factor 0.3t is observed. This suggests that the ``string scenario'' might have some relevance there.
We present analytic and numerical results for the ground state of a dynamical hole in a quantum Ising antiferromagnet (the t-Jz{J}_{z}Jz​ model) on a two-dimensional square lattice. We find that the ground state has a localized region of reduced N\'eel order associated with the hole, with an energy that is well described by ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{h}}$/t\ensuremath{\approxeq}-3.63+2.93(Jz{\mathit{J}}_{\mathit{z}}Jz​/t)23{)}^{23})23 for 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\lesssim}Jz{\mathit{J}}_{\mathit{z}}Jz​/t\ensuremath{\lesssim}1. This resolves a disagreement in the literature regarding the coefficient of (Jz{J}_{z}Jz​/t)2/3{)}^{2/3})2/3. A simple string picture gives a reasonable description of the extent of the ground-state polaron in this intermediate-coupling regime. Disruption of long-range antiferromagnetic order in the bulk limit is estimated to occur at Jz{J}_{z}Jz​/t\ensuremath{\approxeq}0.3 for a hole-doping fraction of x=(1/16.
The spectral functions of one hole in the t-J and one-band Hubbard models are calculated using exact diagonalization techniques on small lattices. Results for the t-Jz{\mathit{J}}_{\mathit{z}}Jz​ model are also presented. For the t-J model we found that there is a quasiparticle at the bottom of the hole spectrum with an energy well approximated by Eh{\mathit{E}}_{\mathit{h}}Eh​=-3.17+2.83J0.73{\mathit{J}}^{0.73}J0.73 (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The rest of the spectrum is not incoherent: We identified at least two other peaks following a similar power-law behavior with J. We speculate that the J dependence of the results can be explained by a model where the hole is trapped in a confining potential as in the Ising limit. The bandwidth of the hole is linear in J in the region 0.1\ensuremath{\le}J\ensuremath{\le}0.4 although a power-law behavior is not excluded. The spectral weight of the quasiparticle grows like J0.5{\mathit{J}}^{0.5}J0.5 in the same region. We present new analytical results in the large J/t limit to understand the motion of the hole: In perturbation theory it can be shown that the momentum of the hole at large J/t is k=(\ensuremath{\pi},\ensuremath{\pi}) changing to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) at intermediate J/t in agreement with numerical and spin-waves results. We show analytically and numerically that the bandwidth of the quasiparticle is of order t in the large J/t limit. This result corresponds to a spin-liquid state. The one-hole spectral function of the Hubbard model is obtained for lattices with 8 and 10 sites. A quasiparticle is also observed in this case. The bandwidth and the relation with the t-J model are discussed and a comparison with recent Monte Carlo results is made. We also review and extend previous results for the ground-state properties of the t-J model.
The motion of a single hole in a Mott antiferromagnet is investigated based on the $t\ensuremath{-}J$ model. An exact expression of the energy spectrum is obtained, in which the irreparable phase string effect [Phys. Rev. Lett. 77, 5102 (1996)] is explicitly present. By identifying the phase string effect with spin backflow, we point out that spin-charge separation must exist in such a system: the doped hole has to decay into a neutral spinon and a spinless holon, together with the phase string. We show that while the spinon remains coherent, the holon motion is deterred by the phase string, resulting in its localization in space. We calculate the electron spectral function which explains the line shape of the spectral function as well as the ``quasiparticle'' spectrum observed in angle-resolved photoemission experiments. Other analytic and numerical approaches are discussed based on the present framework.
The effective Hamiltonian, obtained from the Hubbard model in the strong-coupling limit, is diagonalized exactly for a periodic two-dimensional square lattice of ten sites. We obtain the ground state of the system for any filling of the lattice and the KKK-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio tU\frac{t}{U}Ut​, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing tU\frac{t}{U}Ut​, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of tU\frac{t}{U}Ut​ exists for which pairing of the holes may be possible.
We solved numerically the integral equation for the selfenergy which describes the motion of a single hole in a two-dimensional quantum antiferromagnet (AF) within the selfconsistent Born approximation. This formulation stresses the similarity of the AF-spin polaron with the standard polaron problem. We confine our calculation to finite cluster geometries and compare with results from previous exact diagonalization studies. The spectral function is characterized by a narrow quasiparticle (qp) peak at the low energy side of the spectra, which appears to be well separated from the incoherent band part for large enough J values. For small J we find a reduced width of ~7t for the incoherent band. The bottom of the coherent qp band always occurs at (±π/2, ±π/2). Its bandwidth initially increases with J until J≃t and then decreases as 2t2/J. A complete characterization of our solution is given, including the dispersion relation and effective masses of this quasiparticle. The comparison with exact diagonalization studies for a 4×4 cluster is remarkably good. From our results we see that a lattice of 16×16 sites describes adequately the thermodynamic limit. We conclude that the simple Born approximation is a valuable scheme to characterize the dynamics of one hole in the t-J model. both in the perturbative and the strong coupling regimes.