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Register a new userThermodynamics of the two-dimensional frustrated J1-J2 Heisenberg ferromagnet in the collinear stripe regime: Susceptibility and correlation length
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We calculate the temperature dependence of the correlation length xi and the uniform susceptibility chi_0 of the frustrated J1-J2 square-lattice Heisenberg ferromagnet in the collinear stripe phase using Green-function technique. The height chi_{max} and the position T(chi_{max}) of the maximum in the chi_0(T) curve exhibit a characteristic dependence on the frustration parameter J2/|J1|, which is well described by power laws, chi_{max}=a(J2-J2^c)^{-nu} and T(chi_{max})=b(J_2-J_2^c), where J2^c = 0.4 and nu is of the order of unity.The correlation length diverges at low temperatures as xi propto e^{A/T}, where A increases with growing J2/|J1|. We also compare our results with recent measurements on layered vanadium phosphates and find reasonable agreement.
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We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J3 on the ground state of the spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor interaction J1 and frustrating antiferromagnetic next-nearest-neighbor interaction J2. A third-neighbor exchange J3 might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO4 or LiCu2O2. In particular, we calculate the critical point J2^c as a function of J3, where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J3 the ferro-spiral transition is always continuous and the critical values J2^c of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 lesssim -(0.01...0.02)|J1| the critical value J2^c of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.
The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.
We perform an extensive density matrix renormalization group (DMRG) study of the ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J_2approx 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J_2 the ground state displays signatures of the magnetic order of the sqrt{3}timessqrt{3} and the q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.
The correlated spin dynamics and the temperature dependence of the correlation length $xi(T)$ in two-dimensional quantum ($S=1/2$) Heisenberg antiferromagnets (2DQHAF) on square lattice are discussed in the light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate (CFTD). In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of $xi(T)$ is in agreement with high-temperature expansions, quantum Monte Carlo simulations and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the Non-Linear $sigma$ Model, no evidence of crossover between different quantum regimes is observed.
Searching for spin liquids on the honeycomb J1-J2 Heisenberg model has been attracting great attention in the past decade. In this Paper we investigate the topological properties of the J1-J2 Heisenberg model by introducing nearest-neighbour and next-nearest-neighbour bond parameters. We find that there exist two topologically different phases in the spin disordered regime 0.2<J2/J1<0.5: for J2/J1<0.32, the system is a zero-flux spin liquid which is topological trivial and gapless; for J2/J1>0.32, it is a pi-flux chiral spin liquid, which is topological nontrivial and gapped. These results suggest that there exist two topologically different spin disorder phases in honeycomb J1-J2 Heisenberg model.
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