We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t-J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t-J model on the square lattice.We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t-J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t-J model on the square lattice.

Aug 1, 20184 citations

Dynamic spin susceptibility in the t−J model

Artem Vladimirov, Dieter Ihle, Nikolay M. Plakida

A relaxation-function theory for the dynamic spin susceptibility in the $t\text{\ensuremath{-}}J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperatures. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on ${\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}$. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its $\ensuremath{\omega}/T$ scaling behavior are calculated in a reasonable agreement with experimental and ED data.A relaxation-function theory for the dynamic spin susceptibility in the $t\text{\ensuremath{-}}J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperatures. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on ${\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}$. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its $\ensuremath{\omega}/T$ scaling behavior are calculated in a reasonable agreement with experimental and ED data.

arXiv:0908.2557Physical Review BSep 21, 200945 citations

Rotationally invariant approximation for the two-dimensional t−J model

A. Sherman, Michael Schreiber

Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.

arXiv:cond-mat/0201526Physical review. B, Condensed matterMar 26, 200231 citations

Ground-state phases of the spin- 1 J 1 − J 2 Heisenberg antiferromagnet on the honeycomb lattice

P. H. Y. Li, R. F. Bishop

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling ${J}_{1}>0$ and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling ${J}_{1}>0$ and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

arXiv:1602.08915Physical review. B./Physical review. BJun 28, 201621 citations

Properties of the two-dimensional spin-1/2 Heisenberg model on a honeycomb lattice with interlayer coupling

Löw

The magnetic properties of the two-dimensional S = 1 2 (quantum) antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum-Monte-Carlo algorithm.The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range.For the two-dimensional system the groundstate energy/bond is found to be E hc 0 = -0.36303(13),and the zero temperature staggered magnetization m st = 0.2681(8).For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T /J = 0.695(10).The magnetic properties of the two-dimensional S = 1 2 (quantum) antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum-Monte-Carlo algorithm.The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range.For the two-dimensional system the groundstate energy/bond is found to be E hc 0 = -0.36303(13),and the zero temperature staggered magnetization m st = 0.2681(8).For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T /J = 0.695(10).

Condensed Matter PhysicsJan 1, 200932 citations

Magnetic Properties of t-J Model

Tetsufumi Tanamoto, Kazuhiro Kuboki, Hidetoshi Fukuyama

The dynamical spin susceptibility χ( q , ω), of the t-J model in two-dimensional square lattice have been studied based on the mean field approximation to the slave-boson formalism. The static spin susceptibility, χ( q , 0), and Im χ( q , ω) at various energy, ω, have been calculated. We found; 1) χ(0, 0) has only weak temperature dependence 2) T 1 T ∝( T +θ) for $T\gtrsim0.1{J}$ with θ linearly dependent on the doping rate, δ 3) T 1 T has a minimum at T =(0.1∼0.2) J 4) Im χ( q , ω) at q = Q ≡(π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.The dynamical spin susceptibility χ( q , ω), of the t-J model in two-dimensional square lattice have been studied based on the mean field approximation to the slave-boson formalism. The static spin susceptibility, χ( q , 0), and Im χ( q , ω) at various energy, ω, have been calculated. We found; 1) χ(0, 0) has only weak temperature dependence 2) T 1 T ∝( T +θ) for $T\gtrsim0.1{J}$ with θ linearly dependent on the doping rate, δ 3) T 1 T has a minimum at T =(0.1∼0.2) J 4) Im χ( q , ω) at q = Q ≡(π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.

Journal of the Physical Society of JapanDec 15, 199182 citations

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling

{J}_{1}>0

and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

T\gtrsim0.1{J}

with θ linearly dependent on the doping rate, δ 3) T 1 T has a minimum at T =(0.1∼0.2) J 4) Im χ( q , ω) at q = Q ≡(π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.