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arXiv:cond-mat/9708180 · Physical review. B, Condensed matter

Hole motion in an arbitrary spin background: Beyond the minimal spin-polaron approximation

Matthias Vojta C, K. W. Becker

Published Feb 1, 1998• 18 citations
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Abstract

The motion of a single hole in an arbitrary magnetic background is investigated for the two-dimensional $t\ensuremath{-}J$ model. The wave function of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large-string basis for the limits of a N\'eel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature.

DOI
10.1103/physrevb.57.3099

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The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the $t\ensuremath{-}J$ model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large $J/t$ we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small $J/t$ this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.

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The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.

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Didier Poilblanc, Timothy A. L. Ziman, Heinz J. Schulz +1 more

A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size ${\mathit{N}}_{\mathit{c}}$(${\mathit{J}}_{\mathit{z}}$). Typically, 16- and 26-site clusters give reliable results for ${\mathit{J}}_{\mathit{z}}$>0.75 and ${\mathit{J}}_{\mathit{z}}$>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}${\mathit{J}}_{\mathit{z}}$ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.

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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.

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Dynamics of string-like states of a hole in a quantum antiferromagnet: a diagrammatic Monte Carlo simulation

Nikolaos G Diamantis, Efstratios Manousakis

Abstract The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decades because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green’s function in the t–J model, where the J term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called string excitations found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy–momentum dependence of the main quasiparticle peak and its residue, the internal excitations of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.

New Journal of Physics•Nov 16, 2021•20 citations
The motion of a single hole in an arbitrary magnetic background is investigated for the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. The wave function of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large-string basis for the limits of a N'eel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature.
The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the $t\ensuremath{-}J$ model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large J/tJ/tJ/t we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small J/tJ/tJ/t this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.
The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.
The problem of the single-hole motion in a two-dimensional quantum Heisenberg antiferromagnet is examined in the t-J model. By introducing a kind of slave-fermion representation for Hubbard operators a hole is treated as a spinless fermion strongly interacting with spin-1/2 degrees of freedom. We suggest an analytic approach based on a decoupling procedure for two-time fermionic Green functions that allows us to describe a hole as a magnetic polaron of a minimal size (i.e., involving one-step ``string'' spin excitations) and reproduce the main features characteristic of a one-hole band in a quantum antiferromagnet. A generalization of the procedure in the spirit of the Lanczos approach to extend the internal structure of the magnetic polaron is discussed.
A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size Nc{\mathit{N}}_{\mathit{c}}Nc​(Jz{\mathit{J}}_{\mathit{z}}Jz​). Typically, 16- and 26-site clusters give reliable results for Jz{\mathit{J}}_{\mathit{z}}Jz​>0.75 and Jz{\mathit{J}}_{\mathit{z}}Jz​>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}Jz{\mathit{J}}_{\mathit{z}}Jz​ separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.
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.
Abstract The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decades because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green’s function in the t–J model, where the J term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called string excitations found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy–momentum dependence of the main quasiparticle peak and its residue, the internal excitations of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.