Path integral approach to order by disorder selection in partially polarized quantum spin systems (original) (raw)
Related papers
Diagnosing order by disorder in quantum spin systems
arXiv (Cornell University), 2014
In this paper we study the frustrated J1 − J2 quantum Heisenberg model on the square lattice for J2 > 2J1, in a magnetic field. In this regime the classical system is known to have a degenerate manifold of lowest energy configurations, where standard thermal order by disorder occurs. In order to study its quantum version we use a path integral formulation in terms of coherent states. We show that the classical degeneracy in the plane transverse to the magnetic field is lifted by quantum fluctuations. Collinear states are then selected, in a similar pattern to that set by thermal order by disorder, leaving a Z2 degeneracy. A careful analysis reveals a purely quantum mechanical effect given by the tunneling between the two minima selected by fluctuations. The effective description contains two planar (XY-like) fields conjugate to the total magnetization and the difference of the two sublattice magnetizations. Disorder in either or both of these fields produces the locking of their conjugate observables. Furthermore, within this scenario we argue that the quantum state is close to a product state.
Journal of Physics: Conference Series, 2009
Using the coupled-cluster method for infinite lattices and the exact diagonalization method for finite lattices, we study the influence of an exchange anisotropy ∆ on the groundstate phase diagram of the spin-1/2 frustrated J1-J2 XXZ antiferromagnet on the square lattice. We find that increasing ∆ > 1 (i.e. an Ising type easy-axis anisotropy) as well as decreasing ∆ < 1 (i.e. an XY type easy-plane anisotropy) both lead to a monotonic shrinking of the parameter region of the magnetically disordered quantum phase. Finally, at ∆ c ≈ 1.9 this quantum phase disappears, whereas in the pure XY limit (∆ = 0) there is still a narrow region around J2 = 0.5J1 where the quantum paramagnetic ground-state phase exists.
Magnetic ordering in the three-dimensional site-disordered Heisenberg model
Physical Review B, 1996
simulations have been carried out on a simple cubic ferromagnet with nearest-neighbor interactions. In order to model the effects of site frustration, a fraction f of the sites are occupied at random by moments that couple antiferromagnetically ͑AF͒ to their neighbors. When the concentration of AF sites is less than ϳ 1 6 , the system has one magnetic transition from paramagnet to ferromagnet at a critical temperature T c. For f Ͼ 1 6 the system exhibits a second distinct ordering event at a lower temperature T xy , where the transverse spin components freeze out leading to an increase in total spin length. Below T xy the system is in a mixed state, in that the z components of the spins are ferromagnetically ordered while the transverse components exhibit AF correlations. The approximate magnetic phase diagram for our model is consistent with experimental results on site-disordered systems such as Eu 1Ϫx Gd x S and Fe 3Ϫx Mn x Si.
Disorder effects in the quantum Heisenberg model: Extended dynamical mean-field theory analysis
Physical Review B, 2007
We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearestneighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two-and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin-liquid (where the local spin susceptibility has a non-integer power-low frequency and/or temperature dependence), in the present case this behavior is more elusive unless disorder is very small. This is because the spin-glass transition temperature leaves only an intermediate temperature regime where the system can display the spin-liquid behavior, which turns out to be more apparent in the static than in the dynamical susceptibility.
Competing orders in a frustrated Heisenberg model on the Fisher lattice
2020
We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first neighbor J1J_{1}J1, second neighbor J2J_{2}J2, and third neighbor J3J_{3}J3 exchange couplings, with antiferromagnetic J1J_{1}J1. The classical ground state phase diagram in the J2J_{2}J2-$J_{3}$ plane obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. We find that an order-by-disorder transition driven by thermal as well as quantum fluctuations occurs in the chain phase. Interestingly, the spin wave spectrum of the Neel state displays three Dirac nodal loops out of which two are symmetry protected while for the antiferromagnetic chain phase we find symmetry protected Dirac lines. Furthermore, we investigate the spin S=1/2S=1/2S=1/2 limit employing a bond operator formalism which captures the singlet-triplet dynamics, and find a rich ground state phase diagram host to variety of valence-bond sol...
Order by disorder in the Heisenberg-compass model on the cubic lattice
Starting from an anisotropic super-exchange Hamiltonian as is found for compounds with strongly correlated electrons in multi-orbital bands and subject to strong spin-orbit interaction we calculate the contribution of thermal and quantum spin fluctuations to the free energy. While the mean field solution of ordered states for such systems usually has full rotational symmetry, we show here that the fluctuations lead to a pinning of the spontaneous magnetization along some preferred direction of the lattice. The fluctuations choose preferred directions for the magnetic order parameter amongst the classically degenerate manifold of states.
Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
Physical Review B, 2011
Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J > 0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J > 0 and J < 0, a finitetemperature phase transition with a breaking of the discrete dihedral symmetry group D6 of the model is present. For J < 0, we find a transition temperature T < c /|J| = 1.566 ± 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J > 0 the transition occurs at an extremely low temperature, T > c ≈ 0.0125 J. Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.