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Register a new userDirectional Ordering of Fluctuations in a Two-dimensional Compass Model
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In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in the orbital space and in the real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.
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A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, Neel temperature T_N, specific heat, and uniform static spin susceptibility $chi$ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of T_N on the compass-model interaction is studied. We find that T_N is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of $chi$.
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero temperature the function diverges logarithmically at q=0. Away from Van Hove filling the ground state polarization function exhibits finite peaks at finite wave vectors. A nematic instability driven by a sufficiently strong attraction in the d-wave charge channel thus leads naturally to a spatially modulated nematic state, with a modulation vector that increases in length with the distance from Van Hove filling. Above Van Hove filling, for a Fermi surface crossing the magnetic Brillouin zone boundary, the modulation vector connects antiferromagnetic hot spots with collinear Fermi velocities.
We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes non-local effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat the irreducible vertices of an effective {it single-impurity} problem as small parameters. This provides a very efficient interpolation between band-like weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle.
Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY-model. Specifically, we show that, unlike the SU(2) symmetric Lifshitz case, in the XY-model the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Neel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.
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