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Register a new userComplex Landau Ginzburg Theory of the Hidden Order in URu_2Si_2
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We develop a Landau Ginzburg theory of the hidden order phase and the local moment antiferromagnetic phase of URu_2Si_2. We unify the two broken symmetries in a common complex order parameter and derive many experimentally relevant consequences such as the topology of the phase diagram in magnetic field and pressure. The theory accounts for the appearance of a moment under application of stress and the thermal expansion anomaly across the phase transitions. It identifies the low energy mode which is seen in the hidden order phase near the conmensurate wavector (0,0, 1) as the pseudo-Goldstone mode of the approximate U(1) symmetry.
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Complex electronic matter exhibit subtle forms of self organization which are almost invisible to the available experimental tools, but which have dramatic physical consequences. One prominent example is provided by the actinide based heavy fermion material URu_2Si_2. At high temperature, the U-5f electrons in URu_2Si_2 carry a very large entropy. This entropy is released at 17.5K via a second order phase transition to a state which remains shrouded in mystery, and which was termed a hidden order state. Here we develop a first principles theoretical method to analyze the electronic spectrum of correlated materials as a function of the position inside the unit cell of the crystal, and use it to identify the low energy excitations of the URu_2Si_2. We identify the order parameter of the hidden order state, and show that it is intimately connected with magnetism. We present first principles results for the temperature evolution of the electronic states of the material. At temperature below 70K U-5f electrons undergo a multichannel Kondo effect, which is arrested at low temperature by the crystal field splitting. At lower temperatures, two broken symmetry states emerge, characterized by a complex order parameter psi. A real $psi$ describes the hidden order phase, and an imaginary psi corresponds to the large moment antiferromagnetic phase, thus providing a unified picture of the two broken symmetry phases, which are realized in this material.
We have performed elastic neutron scattering experiments under uniaxial stress sigma applied along the tetragonal [100], [110] and [001] directions for the heavy electron compound URu2Si2. We found that antiferromagnetic (AF) order with large moment is developed with sigma along the [100] and [110] directions. If the order is assumed to be homogeneous, the staggered ordered moment mu_o continuously increases from 0.02 mu_B (sigma=0) to 0.22 mu_B (0.25 GPa). The rate of increase partial mu_o/partial sigma is ~ 1.0 mu_B/GPa, which is four times larger than that for the hydrostatic pressure (partial mu_o/partial P sim 0.25 mu_B/GPa). Above 0.25 GPa, mu_o shows a tendency to saturate, similar to the hydrostatic pressure behavior. For sigma||[001], mu_o shows only a slight increase to 0.028 mu_B (sigma = 0.46 GPa) with a rate of ~ 0.02 mu_B/GPa, indicating that the development of the AF state highly depends on the direction of sigma. We have also found a clear hysteresis loop in the isothermal mu_o(sigma) curve obtained for sigma||[110] under the zero-stress-cooled condition at 1.4 K. This strongly suggests that the sigma-induced AF phase is metastable, and separated from the hidden order phase by a first-order phase transition. We discuss these experimental results on the basis of crystalline strain effects and elastic energy calculations, and show that the c/a ratio plays a key role in the competition between these two phases.
The phase diagram of the quantum spin-1/2 antiferromagnetic $J^{,}_{1}$-$J^{,}_{2}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0leq J^{,}_{2}/J^{,}_{1}<1/2$, i.e., a gapless algebraic spin liquid phase, a gapped long-range ordered Neel phase, and a gapped long-range ordered dimer phase. Even though the Neel and dimer phases are not related hierarchically by a pattern of symmetry breaking, it was shown that they meet along a line of quantum critical points with a U(1) symmetry and central charge $c=1$. Here, we extend the analysis made by Haldane on the quantum spin-1/2 antiferromagnetic $J^{,}_{1}$-$J^{,}_{2}$ XYZ chain using both bosonization and numerical techniques. We show that there are three Neel phases and the dimer phase that are separated from each other by six planes of phase boundaries realizing U(1) criticality when $0leq J^{,}_{2}/J^{,}_{1}<1/2$. We also show that each long-range ordered phase harbors topological point defects (domain walls) that are dual to those across the phase boundary in that a defect in one ordered phase locally binds the other type of order around its core. By using the bosonization approach, we identify the critical theory that describes simultaneous proliferation of these dual point defects, and show that it supports an emergent U(1) symmetry that originates from the discrete symmetries of the XYZ model. To confirm this numerically, we perform DMRG calculation and show that the critical theory is characterized by the central charge $c=1$ with critical exponents that are consistent with those obtained from the bosonization approach. Furthermore, we generalize the field theoretic description of direct continuous phase transition to higher dimensions, especially in $d=3$, by using a non-linear sigma model (NLSM) with a topological term.
Hidden-order phase transition in the heavy-fermion superconductor URu$_2$Si$_2$ exhibits the mean-field-like anomaly in temperature dependence of heat capacity. Motivated by this observation, here we explore the impact of the complex order parameter fluctuations on the thermodynamic properties of the hidden order phase. Specifically, we employ the mean-field theory for the hidden order which describes the hidden order parameter by an average of the hexadecapole operator. We compute the gaussian fluctuation corrections to the mean-field theory equations including both the fluctuations due to hidden order as well as antiferromagnetic order parameters. We find that the gaussian fluctuations lead to the smearing of the second-order transition rendering it to become the first-order one. The strength of the first-order transition is weakly dependent on the strength of underlying antiferromagnetic exchange interactions.
The complex Ginzburg-Landau equation (CGLE) is a general model of spatially extended nonequilibrium systems. In this paper, an analytical method for a variable coefficient CGLE is presented to obtain exact solutions. Variable transformations for space and time variables with coefficient functions yield an imaginary time advection equation related to a complex valued characteristic curve. The variable coefficient CGLE is transformed into the nonlinear Schr{o}dinger equation (NLSE) on the complex valued characteristic curve. This result indicates that the analytical solutions of the NLSE generate that of the variable coefficient CGLE.
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