Spontaneous plaquette dimerization in the J1-J2 heisenberg model

We investigate the nonmagnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected "plaquette resonating valence bond," with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J(2)/J(1) approximately 0.5.     

Ising transition in the two-dimensional quantum J1-J2 Heisenberg model

We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings in its collinear phase (J(2)/J(1)>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J(2)/J(1) is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin and temperature dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li2VOSiO4 and related compounds.     

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

We study the ground-state phase diagram of the frustrated spin-[Formula: see text] antiferromagnet with J(2) = xJ(1) > 0 (J(1) > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x(c(1)) < x < x(c(2)), where x(c(1)) ≈ 0.207 ± 0.003 and x(c(2)) ≈ 0.385 ± 0.010. The transition at x(c(1)) to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ? x ? 0.24), while that at x(c(2)) is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point [Formula: see text]. The spiral phases that are present classically for all values x > 1/6 are absent for all x ? 1.     

Symmetry breaking in the collinear phase of the J1-J2 Heisenberg model

The large J2 limit of the square-lattice J1-J2 Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a mean-field spin-wave theory to study the excitation spectra in this phase and look for a finite-temperature Ising-like transition, corresponding to a broken symmetry of the square lattice, as first proposed by Chandra et al. [Phys. Rev. Lett. 64, 88 (1990)]]. We find that the spectra reveal the symmetries of the ordered phase. However, we do not find evidence for a finite-T transition. We suggest a scenario for a T=0 transition based on quantum fluctuations.     

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J1-J2 Heisenberg model

Restricted Boltzmann machine (RBM) has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system. On the other hand, as a shallow neural network, it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions. In order to find a way out of the dilemma, here, we propose to adopt the Green's function Monte Carlo (GFMC) method for which the RBM is used as a guiding wave function. To demonstrate the implementation and effectiveness of the proposal, we have applied the proposal to study the frustrated J₁-J₂ Heisenberg model on a square lattice, which is considered as a typical model with sign problem for quantum Monte Carlo simulations. The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results. This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Magnetic susceptibility and short-range order in iron pnictides: Anisotropic J1-J2 Heisenberg model

The electron spin relaxation times by piezoelectric and polar optical phonon scattering in GaAs are calculated using the formula derived from the projection-reduction method. The temperature, magnetic field, and electron density dependences of the relaxation time are investigated. The electrons are found to be scattered mostly by piezoelectric phonons at low temperatures and polar optical phonons at high temperatures. The electron density affects the magnetic field dependence of the relaxation time at low temperatures but have only slight affects at high temperatures.     

Approximate ground state in a model with spontaneous symmetry breakdown

The spontaneous symmetry breakdown is treated by means of a variational approach. Use is made of coherent states of Glauber and of pairing states of BCS-type as the translationally invariant vacuum states for the discussion of the real scalar field ⁴ withm ₀ ² 0. The first type of trial states reproduces the usual approach to spontaneous symmetry breakdown (-) in the tree approximation (which is possible only form ₀ ² <0), while the second type of trial states offers the possibility of spontaneous symmetry breakdown even form ₀ ² =0.     

The Ising model on the layered J1-J2 square lattice

We investigate the phase transitions in the Ising model on a layered square lattice with first-($J_1$) and second-($J_2$) neighbor intralayer interactions and interlayer couplings (J). The thermodynamics of the system is evaluated within a cluster mean-field approximation, which allows us to identify the nature of the thermally driven phase transitions hosted by the model. As a result, we find that interlayer couplings reduce the region of first-order phase transitions between paramagnetic and superantiferromagnetic states. We also find that the interlayer couplings reduce the frustration effects by reducing the entropy content of the low-temperature phases. Our results suggest that tricriticality is present in the special case $J=J_1$, which is in qualitative agreement with recent Monte Carlo simulations for the model.     

Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: The sigma model sector and the kink sector

We identify two distinct low-energy sectors in the classical isotropic antiferromagnetic Heisenberg spin-S chain, in the continuum limit. We show that two types of rotation generators arise for the field in each sector. Using these, the Lagrangian for sector I is shown to be that of the nonlinear sigma model. Sector II has a null Lagrangian. Its Hamiltonian density is just the Pontryagin term. Exact solutions are found in the form of magnons and precessing pulses in I and moving kinks in II. The kink has ‘spin’ S. Sector I has a higher minimum energy than II.     

Off-diagonal long-range order in the ground state of the two-dimensional antiferromagnetic Heisenberg model

A two-dimensional Jordan-Wigner transformation, together with a fermion-boson mapping, has been used to transform the two-dimensional antiferromagnetic Heisenberg model (2D AFMHM) into an interacting boson system with a fixed number of particles. We found that the excitation energy depends linearly on the momentum for small energy, and it is 1.80J for (π,π). Our results suggest that the ground state of the 2D AFMHM is a quantum liquid, and the order is off-diagonal long-range order associated with the Bose-Einstein condensation.