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arXiv:cond-mat/0304204 · Physical review. B, Condensed matter

Effects of domain walls on hole motion in the two-dimensional anisotropic t−J model at finite temperature

José A. Riera

Published Aug 26, 2003• 0 citations
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Abstract

The $t\ensuremath{-}J$ model on the square lattice, close to the $t\ensuremath{-}{J}_{z}$ limit, is studied by quantum Monte Carlo techniques at finite temperature and in the underdoped regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify the antiferromagnetic domains on each Trotter slice. The results show that the model at high enough temperature presents finite antiferromagnetic (AF) domains, which collapse at lower temperatures into a single ordered AF state. While there are domains, holes would tend to preferentially move along the domain walls. In this case, there are indications of hole pairing starting at a relatively high temperature. At lower temperatures, when the whole system becomes essentially fully AF ordered, at least in finite clusters, holes would likely tend to move within phase separated regions. The crossover between both states moves down in temperature as doping increases and/or as the off-diagonal exchange increases. The possibility of hole motion along AF domain walls at zero temperature in the fully isotropic $t\ensuremath{-}J$ is discussed.

DOI
10.1103/physrevb.68.054530

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The t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model on the square lattice, close to the t\ensuremath−Jzt\ensuremath{-}{J}_{z}t\ensuremath−Jz​ limit, is studied by quantum Monte Carlo techniques at finite temperature and in the underdoped regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify the antiferromagnetic domains on each Trotter slice. The results show that the model at high enough temperature presents finite antiferromagnetic (AF) domains, which collapse at lower temperatures into a single ordered AF state. While there are domains, holes would tend to preferentially move along the domain walls. In this case, there are indications of hole pairing starting at a relatively high temperature. At lower temperatures, when the whole system becomes essentially fully AF ordered, at least in finite clusters, holes would likely tend to move within phase separated regions. The crossover between both states moves down in temperature as doping increases and/or as the off-diagonal exchange increases. The possibility of hole motion along AF domain walls at zero temperature in the fully isotropic t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J is discussed.
Finite temperature quantum Monte Carlo simulations are performed on the anisotropic $t\ensuremath{-}J$ model and in particular on its Ising limit. Straight site-centered stripes are imposed by an on-site potential representing external mechanisms of stripe formation. In this model, we show that, even though charge inhomogeneity exists at a high temperature, the antiphase ordering of the spin domains between stripes occurs at a much lower temperature. The magnetic correlations at this spin ordering crossover are analyzed. The stripes show metallicity, with absence of hole attraction. Comparison between this model and others that have been proposed to explain or describe stripes, as well as possible relations with experimental features on underdoped cuprates are discussed.
We study a two-dimensional $t\ensuremath{-}J$ model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential es,{e}_{s},es​, by using diagonalization in a restricted Hilbert space and finite temperature quantum Monte Carlo techniques. Both site- and bond-centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as ${e}_{s}\ensuremath{\rightarrow}0.$ Moreover, we show that the antiphase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic behavior of the stripes with no signs of hole attraction. Kinetic energies and current susceptibilities are computed and indications of charge localization are discussed. The study of the doping dependence in the range 0.083< x< 0.1670.083<~x<~0.1670.083< x< 0.167 suggests that these features are characteristic of the whole underdoped region.
Hole-density correlation functions in the t-J model on lattices with square geometry are studied by the method of exact diagonalization for systems of various sizes with up to 26 sites. For the largest sizes we employ only a restricted basis, whereby for the extrapolation we introduce and test a scaling procedure. For two holes in an antiferromagnet our results confirm their binding for J>Jc{\mathit{J}}_{\mathit{c}}Jc​\ensuremath{\sim}0.2t. For four holes the two-point and four-point density correlations, calculated for N=18,20 sites, show clear evidence for hole-clustering instabilities for J>Js{\mathit{J}}_{\mathit{s}}Js​\ensuremath{\sim}1.5t; a first instability is likely to be towards a striped phase, with holes forming domain walls along the (0,1) or (1,0) direction. Signs for the phase separation into a hole-rich and a hole-free phase appear only at J>Js∗{\mathit{J}}_{\mathit{s}}^{\mathrm{*}}Js∗​\ensuremath{\sim}2.5t. Results in the intermediate regime 0.4J/t1.2 are consistent with the pairing picture, although there are also indications for a large weight of configurations representing domain walls along the (1,1) direction.
The $t\ensuremath{-}{J}_{z}$ model is the strongly anisotropic limit of the $t\ensuremath{-}J$ model which captures some general properties of doped antiferromagnets (AF's). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p- and d-wave channels at realistic values of t/J.t/J.t/J. Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic $t\ensuremath{-}J$-like model. Possible implications for preformed pairs formation and phase separation are drawn.
Candidates for the ground state of the anisotropic t-Jz{\mathit{J}}_{\mathit{z}}Jz​ model at low hole doping are studied within two related lattices: the Cayley tree and the square lattice. The Cayley tree allows for the evaluation of the single hole as well as the hole-pair ground states to arbitrary precision. Threshold values for the formation of bound hole pairs appear to be similar for both lattices. We show that the main contributions to the binding of a hole pair on the Cayley tree comes from the excess number of frustrated bonds (``spinons''). Considering systems with a larger number of holes, we establish high stability of configurations with holes forming straight domain walls between nonequivalent antiferromagnetic domains. In particular, for the Cayley tree we find that domain-wall-like configurations have lower energy than separate hole pairs. For the square lattice, however, there exists at low but finite doping a parameter interval 0.18J/t0.56 where, in the ground state, holes are paired.
We study the phase diagram of the two-dimensional t-J-V model of holes in a two-dimensional antiferromagnet in the J\ensuremath{\gg}t limit. Here t is the hole hopping parameter, J is the exchange coupling between nearest-neighbor spins, and V is the nearest-neighbor electron-electron repulsion. We also include the possibility of Heisenberg-Ising anisotropy, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ne}Jz{\mathit{J}}_{\mathit{z}}Jz​. We obtain a complete description for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ll}Jz{\mathit{J}}_{\mathit{z}}Jz​ and approximate results for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=Jz{\mathit{J}}_{\mathit{z}}Jz​. There is no region of the zero-temperature phase diagram that supports a dilute gas of holes in an antiferromagnet. Rather, the system always phase separates into hole-rich and no-hole phases, a result we believe to be more general than the model we have considered. We find various hole-crystal phases and, at high hole density, we find a ``Fermi-liquid'' phase and at least two superfluid phases, one with a charge 2e and one with a charge 4e order parameter.