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

Mobile vacancy in a quantum antiferromagnet: Effective Hamiltonian

Boris I. Shraiman, Eric D. Siggia

Published Aug 1, 1990• 90 citations
Publisher

Abstract

A semiclassical analysis, as well as symmetry considerations, are used to explain and extend published quantum-cluster results for the ground state of a hole in a quantum antiferromagnet (AF). For the ground state with a wave vector in the face center of the reduced Brillouin zone, the spins twist into a dipolar configuration around the hole to optimize the hopping term, but remain coplanar. More complicated three-dimensional spin textures with staggered topological charge can be constructed by superimposing dipole states corresponding to distinct points in the Brillouin zone and different planes of spin twist. An effective Hamiltonian for the hole that generalizes the nonlinear sigma model is derived. The essential new term that is responsible for the textures described is a coupling between spin currents for the holes and background spins. The presence of the local antiferromagnetic correlations dictates a spinor representation of the vacancy. This description provides the foundation for the study of the phases of a quantum AF at low vacancy density.

DOI
10.1103/physrevb.42.2485

Related papers

Ground state of a mobile vacancy in a quantum antiferromagnet: Small-cluster study

Veit Elser, David A. Huse, Boris I. Shraiman +1 more

The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.

Physical review. B, Condensed matter•Apr 1, 1990•77 citations

Small-cluster study of a single-holet-Jmodel

Tao Xiang

We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).

Physical review. B, Condensed matter•Aug 1, 1991•7 citations

Spin Correlations around Mobile Holes in an Antiferromagnet

Jun-ichiro Inoue, Sadamichi Maekawa

Various spin correlation functions around a mobile hole in a two-dimensional antiferromagnetic state are calculated in the t - J model. The correlations show canted and twisted character at k =(0, 0) and (π/2, π/2), respectively, where the latter is the wave vector of the ground state. Possible spin configurations around the hole are discussed.

Journal of the Physical Society of Japan•Oct 15, 1990•9 citations

Quasihole excitation in a quantum antiferromagnet: Variational Monte Carlo calculation

Massimo Boninsegni, Efstratios Manousakis

We study a single quasihole excitation in a quantum antiferromagnet using a variational wave function that includes spin-spin as well as spin-hole correlations. The wave function can be cast in the form of a complex correlation operator acting on a Marshall-type wave function for the spin background. Such a correlation operator, featuring momentum-dependent spin-hole correlations, is shown to correspond to a coherent local rotation of the spins, which can be also interpreted as a ``spin-backflow'' current, analogous to the Feynman-Cohen backflow current in helium liquids. The variational Monte Carlo method is used to calculate the hole excitation spectrum on a square lattice for the t-J model with this wave function. Comparing our results with available exact results on a 4\ifmmode\times\else\texttimes\fi{}4 square lattice, we find qualitative and semiquantitative agreement. We provide results obtained on much larger lattices. We find that the quasihole energy band attains its minimum at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) while the hole mass is strongly anisotropic in different directions of k space. The quasihole excitation creates both a planar long-range distortion of the antiferromagnetic (AF) moment of the background \ensuremath{\delta}${\mathit{m}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(r\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}(k\ensuremath{\cdot}r)/${\mathit{r}}^{2}$ and a ferromagnetic moment localized in the immediate neighborhood of the hole, pointing in the perpendicular direction. The magnitude of the ferromagnetic moment depends on the momentum of the excitation, and at the minimum of the hole band only the long-range AF planar distortion is present.

Physical review. B, Condensed matter•May 1, 1991•42 citations

Charge and spin quantum fluctuations in the doped strongly coupled Hubbard model on the honeycomb lattice

F. G. Ribeiro, Mauricio D. Coutinho-Filho

Field-theoretic methods are used to investigate the large-$U$ Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge and spin degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the quantum antiferromagnetic phase (AF) as a function of hole doping. At half-filling, we deal with the underlying spin degrees of freedom of the quantum AF Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear $\ensuremath{\sigma}$ model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. Lastly, in the challenging doped regime, our approach allows the derivation of a $t\text{\ensuremath{-}}J$ Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations.

Physical Review B•Jul 6, 2015•2 citations

Study of the excited states of the quantum antiferromagnets

Mohammad G. Merdan

We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone $\Gamma(\mathbf q=0)$ and at the magnetic ordering wavevectors $\pm[\mathbf Q= (4\pi/3,0)]$, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.

•Nov 10, 2013•0 citations
A semiclassical analysis, as well as symmetry considerations, are used to explain and extend published quantum-cluster results for the ground state of a hole in a quantum antiferromagnet (AF). For the ground state with a wave vector in the face center of the reduced Brillouin zone, the spins twist into a dipolar configuration around the hole to optimize the hopping term, but remain coplanar. More complicated three-dimensional spin textures with staggered topological charge can be constructed by superimposing dipole states corresponding to distinct points in the Brillouin zone and different planes of spin twist. An effective Hamiltonian for the hole that generalizes the nonlinear sigma model is derived. The essential new term that is responsible for the textures described is a coupling between spin currents for the holes and background spins. The presence of the local antiferromagnetic correlations dictates a spinor representation of the vacancy. This description provides the foundation for the study of the phases of a quantum AF at low vacancy density.
The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.
We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).
We study a single quasihole excitation in a quantum antiferromagnet using a variational wave function that includes spin-spin as well as spin-hole correlations. The wave function can be cast in the form of a complex correlation operator acting on a Marshall-type wave function for the spin background. Such a correlation operator, featuring momentum-dependent spin-hole correlations, is shown to correspond to a coherent local rotation of the spins, which can be also interpreted as a ``spin-backflow'' current, analogous to the Feynman-Cohen backflow current in helium liquids. The variational Monte Carlo method is used to calculate the hole excitation spectrum on a square lattice for the t-J model with this wave function. Comparing our results with available exact results on a 4\ifmmode\times\else\texttimes\fi{}4 square lattice, we find qualitative and semiquantitative agreement. We provide results obtained on much larger lattices. We find that the quasihole energy band attains its minimum at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) while the hole mass is strongly anisotropic in different directions of k space. The quasihole excitation creates both a planar long-range distortion of the antiferromagnetic (AF) moment of the background \ensuremath{\delta}${\mathit{m}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(r\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\sim}(k\ensuremath{\cdot}r)/r2{\mathit{r}}^{2}r2 and a ferromagnetic moment localized in the immediate neighborhood of the hole, pointing in the perpendicular direction. The magnitude of the ferromagnetic moment depends on the momentum of the excitation, and at the minimum of the hole band only the long-range AF planar distortion is present.
Field-theoretic methods are used to investigate the large-UUU Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge and spin degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the quantum antiferromagnetic phase (AF) as a function of hole doping. At half-filling, we deal with the underlying spin degrees of freedom of the quantum AF Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear $\ensuremath{\sigma}$ model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. Lastly, in the challenging doped regime, our approach allows the derivation of a $t\text{\ensuremath{-}}J$ Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.