Physical review. B, Condensed matter

Dispersion relation of a single hole in thet-Jmodel determined by a variational Monte Carlo method

Thierry Giamarchi, C. Lhuillier

Published Feb 1, 1993• 15 citations

Abstract

We use a simple Gutzwiller variational wave function to study the dispersion relation of one single hole in the t-J model. Such a wave function gives a minimum of energy for the hole at (\ensuremath{\pi}/2,\ensuremath{\pi}/2), in agreement with previous results, and both a band width and an energy that are linear in J for moderate values of J.

DOI: 10.1103/physrevb.47.2775

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Physical review. B, Condensed matter

Dispersion relation of a single hole in thet-Jmodel determined by a variational Monte Carlo method

Thierry Giamarchi, C. Lhuillier

Published Feb 1, 1993• 15 citations

Publisher

Abstract

DOI: 10.1103/physrevb.47.2775

Related papers

Two-holed-wave binding in the physical region of thet-Jmodel: A Green’s-function Monte Carlo study

Massimo Boninsegni, Efstratios Manousakis

We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$ \ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J ${\mathit{J}}_{\mathit{c}}$ .We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J${\mathit{J}}_{\mathit{c}}$.

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Monte Carlo study of one-hole band structure in thet-Jmodel

Ted Barnes, Mitchel D. Kovarik

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B. M. Elrick, Allan E. Jacobs

We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over ${10}^{6}$ states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over ${10}^{6}$ states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.

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Dispersion of a single hole in the t-J model

Ting-Kuo Lee, C. T. Shih

The dispersion of a single hole in the t-J model obtained by the exact result of 32 sites and the results obtained by self-consistent Born approximation and the Green function Monte Carlo method can be simply derived by a mean-field theory with d-wave resonating-valence-bond (d-RVB) and antiferromagnetic order parameters. In addition, it offers a simple explanation for the difference observed between those results. The presence of the extended van Hove region at (\ensuremath{\pi},0) is a consequence of the d-RVB pairing instead of the antiferromagnetic order. Results including ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ and ${\mathrm{t}}^{|\mathrm{I}\mathrm{J}}$ are also presented and explained consistently in a similar way.The dispersion of a single hole in the t-J model obtained by the exact result of 32 sites and the results obtained by self-consistent Born approximation and the Green function Monte Carlo method can be simply derived by a mean-field theory with d-wave resonating-valence-bond (d-RVB) and antiferromagnetic order parameters. In addition, it offers a simple explanation for the difference observed between those results. The presence of the extended van Hove region at (\ensuremath{\pi},0) is a consequence of the d-RVB pairing instead of the antiferromagnetic order. Results including ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ and ${\mathrm{t}}^{|\mathrm{I}\mathrm{J}}$ are also presented and explained consistently in a similar way.

arXiv:cond-mat/9604061Physical review. B, Condensed matterMar 1, 199769 citations

Single-hole effective masses in thet-Jmodel

X. Zotos, P. Prelovek, Igor Sega

The ground state of a single hole in the one- and two-dimensional t-J model is studied for finite systems as a function of the phase in the kinetic energy term. The coherent effective hopping ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$ and the incoherent hopping ${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$ , evaluated in this way, are connected via the conductivity sum rule. It is shown that for even and odd chains ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$ \ensuremath{\sim} ${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$ , while their reduction from the free value t remains small even for large J/t. The Bethe ansatz solution, obtained for J=2t, is consistent with the latter result, yielding ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$ /t\ensuremath{\sim}0.938. In the 4\ifmmode\times\else\texttimes\fi{}4 system, the phase variation yields a nontrivial energy manifold. The minimum appears to be near the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},0) line in the Brillouin zone for J/t1, while moving towards the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},\ensuremath{\pi}) line for J/t\ensuremath{\gg}1.The ground state of a single hole in the one- and two-dimensional t-J model is studied for finite systems as a function of the phase in the kinetic energy term. The coherent effective hopping ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$ and the incoherent hopping ${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$, evaluated in this way, are connected via the conductivity sum rule. It is shown that for even and odd chains ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$\ensuremath{\sim}${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$, while their reduction from the free value t remains small even for large J/t. The Bethe ansatz solution, obtained for J=2t, is consistent with the latter result, yielding ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$/t\ensuremath{\sim}0.938. In the 4\ifmmode\times\else\texttimes\fi{}4 system, the phase variation yields a nontrivial energy manifold. The minimum appears to be near the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},0) line in the Brillouin zone for J/t1, while moving towards the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},\ensuremath{\pi}) line for J/t\ensuremath{\gg}1.

Physical review. B, Condensed matterNov 1, 199053 citations

We investigate numerically the ground state of two holes with

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value

{\mathit{J}}_{\mathit{c}}

\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J

{\mathit{J}}_{\mathit{c}}

We present Monte Carlo results for the band structure of the lowest-lying

{\mathit{S}}_{\mathrm{tot}}

=1/2 one-hole band in the t-J model on 4\ifmmode\times\else\texttimes\fi{}4 and 6\ifmmode\times\else\texttimes\fi{}6 lattices. In this paper we report measurements for all k states in the small t/J regime 0\ensuremath{\le}t/J\ensuremath{\le}0.2, and extrapolate to 0\ensuremath{\le}t/J\ensuremath{\le}0.5. Our results support the conjecture that the linear-t component of the bandwidth at small t/J vanishes as \ensuremath{\kappa}/

{\mathit{L}}^{2}

in the bulk limit, as was anticipated on theoretical grounds; this implies that the propagation of isolated holes is strongly hindered by the staggered magnetization of the ground state. For this initial study we used a very simple trial wave function for importance sampling; it should be possible to obtain comparably accurate Monte Carlo results for band structure at appreciably larger t/J with improved importance sampling.

We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over

{10}^{6}

states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.

{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}

and

{\mathrm{t}}^{|\mathrm{I}\mathrm{J}}

are also presented and explained consistently in a similar way.

The ground state of a single hole in the one- and two-dimensional t-J model is studied for finite systems as a function of the phase in the kinetic energy term. The coherent effective hopping

{\mathit{t}}_{\mathit{c}}^{\mathrm{*}}

and the incoherent hopping

{\mathit{t}}_{\mathit{i}}^{\mathrm{*}}

, evaluated in this way, are connected via the conductivity sum rule. It is shown that for even and odd chains

{\mathit{t}}_{\mathit{c}}^{\mathrm{*}}

\ensuremath{\sim}

{\mathit{t}}_{\mathit{i}}^{\mathrm{*}}

, while their reduction from the free value t remains small even for large J/t. The Bethe ansatz solution, obtained for J=2t, is consistent with the latter result, yielding

{\mathit{t}}_{\mathit{c}}^{\mathrm{*}}

/t\ensuremath{\sim}0.938. In the 4\ifmmode\times\else\texttimes\fi{}4 system, the phase variation yields a nontrivial energy manifold. The minimum appears to be near the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},0) line in the Brillouin zone for J/t1, while moving towards the (\ensuremath{\pi}/2,\ensuremath{\pi}/2)-(\ensuremath{\pi},\ensuremath{\pi}) line for J/t\ensuremath{\gg}1.