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

Physical review. B, Condensed matter

Geometry-controlled conserving approximations for thet-Jmodel

M. D. Johnson, Claudius Gros, K. J. von Szczepanski

Published May 1, 1991• 14 citations
Publisher

Abstract

We present in detail a Green's-function approach for studying charged-spin systems which preserves the local constraints prohibiting double occupancy. This approach satisfies Wick's theorem, uses a fermionic expansion around a singly occupied N\'eel state, and treats charge and spin degrees of freedom on an equal footing. For the antiferromagnetic Heisenberg model we recover gapless spin excitations (renormalized spin waves) in a straightforward real-space random-phase-approximation approach. This expansion is strictly controlled by a geometrical factor, 1/z, where z is the coordination number. We describe the incoherent motion of charges (holes) in the t-J model by a self-retracing-path approximation and consider two competing contributions to the coherent hole propagation. These approximations are made conserving in a constructive fashion by mapping Feynman diagrams to an equivalent tight-binding model. To study the accuracy of this procedure, we have made a detailed numerical check against the results obtained by exact diagonalization of a 4\ifmmode\times\else\texttimes\fi{}4 system with one hole, finding excellent agreement both in and near the Ising limit.

DOI
10.1103/physrevb.43.11207

Related papers

Wick’s theorem for charged spin systems

Claudius Gros, M. D. Johnson

We present a new Green's-function approach to charged spin systems which preserves the local constraints prohibiting double occupancy. It is a systematic fermionic expansion and yields 1/(2z) as a control parameter for the Heisenberg model. For the t-J model the spin and hole Green's functions are treated on an equal footing. In the Ising limit, the Brinkman-Rice approximation and a bandwidth \ensuremath{\sim}${J}^{z}$ are recovered for, respectively, the incoherent and coherent hole motion. A new picture for the coherent hole propagation is obtained in the Heisenberg limit.

Physical review. B, Condensed matter•Nov 1, 1989•42 citations

Dynamics of a hole in thet-Jmodel with local disorder: Exact results for high dimensions

Rainer Strack, D. Vollhardt

We investigate the t-J model including local disorder for a hole in an antiferromagnetic spin background on a hypercubic lattice in d dimensions. We show that the well-known approximation of a linear potential, caused by the Ising term of the spin-spin interaction, is correct up to order 1/${\mathit{d}}^{2}$ and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/${\mathit{d}}^{4}$.

Physical review. B, Condensed matter•Dec 1, 1992•50 citations

Dynamical properties of a hole in a Heisenberg antiferromagnet

Zhiping Liu, Efstratios Manousakis

The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.

Physical review. B, Condensed matter•Feb 1, 1992•274 citations

Mapping spin-charge separation without constraints

Chandler, J. I., Gunn, J. M. F.

The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local `spin'-1/2 operators is derived. The electron Hilbert space is mapped onto a tensor productspin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the ``pseudospin'' used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects.

arXiv:cond-mat/9702009•Jan 31, 1997•0 citations

Perturbation formalism of an exact representation for thet-Jmodel

Zhe Chang

We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-${\mathit{T}}_{\mathit{c}}$ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jan 15, 1996•9 citations

Loop-expansion study of the single-hole spectral function in thet-Jmodel

Zhiping Liu, Efstratios Manousakis

We consider a single hole in the t-J model where the Heisenberg and the hole-hopping terms are expanded in powers of the spin-deviation operators. The lowest order corresponds to the linear spin-wave approximation and leads to an effective Hamiltonian studied earlier by means of self-consistent perturbation theory. In this work we shall include all terms generating up to two-loop diagrams in the perturbative expansion of the single-hole Green's function. The hard-core constraints are partially respected and the overall effect gives a renormalization factor of 1.158 to the hopping parameter t. The vertex that describes the process where a spin wave is absorbed and emitted at the same time by the hole is far more important than others. We find that the numerical solutions of Dyson's equation including all two-loop diagrams lower considerably the single-hole ground-state energies over the previous one-loop results and our results on the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in better agreement with those obtained by exact diagonalization in the physical regime (small J/t). Our method can provide numerical solutions to the hole Green's function on very large lattices. We find that with the inclusion of the two-loop diagrams the spectral function retains all its features found in the one-loop calculation and the bandwidth, the quasiparticle residues, and the ``string'' excitations feel very small corrections.

Physical review. B, Condensed matter•Feb 1, 1995•23 citations
We present in detail a Green's-function approach for studying charged-spin systems which preserves the local constraints prohibiting double occupancy. This approach satisfies Wick's theorem, uses a fermionic expansion around a singly occupied N'eel state, and treats charge and spin degrees of freedom on an equal footing. For the antiferromagnetic Heisenberg model we recover gapless spin excitations (renormalized spin waves) in a straightforward real-space random-phase-approximation approach. This expansion is strictly controlled by a geometrical factor, 1/z, where z is the coordination number. We describe the incoherent motion of charges (holes) in the t-J model by a self-retracing-path approximation and consider two competing contributions to the coherent hole propagation. These approximations are made conserving in a constructive fashion by mapping Feynman diagrams to an equivalent tight-binding model. To study the accuracy of this procedure, we have made a detailed numerical check against the results obtained by exact diagonalization of a 4\ifmmode\times\else\texttimes\fi{}4 system with one hole, finding excellent agreement both in and near the Ising limit.
We present a new Green's-function approach to charged spin systems which preserves the local constraints prohibiting double occupancy. It is a systematic fermionic expansion and yields 1/(2z) as a control parameter for the Heisenberg model. For the t-J model the spin and hole Green's functions are treated on an equal footing. In the Ising limit, the Brinkman-Rice approximation and a bandwidth \ensuremath{\sim}Jz{J}^{z}Jz are recovered for, respectively, the incoherent and coherent hole motion. A new picture for the coherent hole propagation is obtained in the Heisenberg limit.
We investigate the t-J model including local disorder for a hole in an antiferromagnetic spin background on a hypercubic lattice in d dimensions. We show that the well-known approximation of a linear potential, caused by the Ising term of the spin-spin interaction, is correct up to order 1/d2{\mathit{d}}^{2}d2 and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/d4{\mathit{d}}^{4}d4.
The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 42{4}^{2}42 lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.
The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local `spin'-1/2 operators is derived. The electron Hilbert space is mapped onto a tensor productspin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the ``pseudospin'' used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects.
We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.
We consider a single hole in the t-J model where the Heisenberg and the hole-hopping terms are expanded in powers of the spin-deviation operators. The lowest order corresponds to the linear spin-wave approximation and leads to an effective Hamiltonian studied earlier by means of self-consistent perturbation theory. In this work we shall include all terms generating up to two-loop diagrams in the perturbative expansion of the single-hole Green's function. The hard-core constraints are partially respected and the overall effect gives a renormalization factor of 1.158 to the hopping parameter t. The vertex that describes the process where a spin wave is absorbed and emitted at the same time by the hole is far more important than others. We find that the numerical solutions of Dyson's equation including all two-loop diagrams lower considerably the single-hole ground-state energies over the previous one-loop results and our results on the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in better agreement with those obtained by exact diagonalization in the physical regime (small J/t). Our method can provide numerical solutions to the hole Green's function on very large lattices. We find that with the inclusion of the two-loop diagrams the spectral function retains all its features found in the one-loop calculation and the bandwidth, the quasiparticle residues, and the ``string'' excitations feel very small corrections.