Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCrossovers due to anisotropy and disorder in quantum critical fluctuations
312
0
0.0
(
0
)
Authors
Chandra M. Varma
Ask ChatGPT about the research
No Arabic abstract
Scaling relations are used to study cross-overs, due to anisotropic spin interactions or single ion anisotropy, and due to disorder, in the thermodynamics and correlation functions near quantum-critical transitions. The principal results are simple with a wide range of applications. The region of attraction to the stable anisotropic fixed point in the quantum-critical region is exponentially enhanced by the dynamical critical exponent $z$ compared to the region of attraction to the fixed point in the quantum disordered region. The result implies that, even for small anisotropy, the region of attraction to the stable incommensurate Ising or planar metallic anti-ferromagnetic critical points, which belong to the universality class of the XY model with $z to infty$, covers the entire quantum-critical region. In crossovers due to disorder, the instability of the pure fixed point in the quantum disordered region is exponentially enhanced by $z$ compared to that in the quantum-critical region. This result suggests that for some classes of disorder and for large enough $z$, one may find singularities in the correlations as a function of frequency and temperature down to very low temperatures even though the correlation length in space remains short range.
rate research
Read More
Quantum criticality in iron pnictides involves both the nematic and antiferromagnetic degrees of freedom, but the relationship between the two types of fluctuations has yet to be clarified. Here we study this problem in the presence of a small external uniaxial potential, which breaks the $C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects the spin excitation anisotropy, which is the difference of the dynamical spin susceptibilities at $vec{Q}_1=left(pi,0right)$ and $vec{Q}_2=left(0,piright)$, with the dynamical magnetic susceptibility and static nematic susceptibility. Using this identity, we introduce a scaling procedure to determine the dynamical nematic susceptibility in the quantum critical regime, and illustrate the procedure for the case of the optimally Ni-doped BaFe$_2$As$_2$[Y. Song textit{et al.}, Phys. Rev. B 92, 180504 (2015)]. The implications of our results for the overall physics of the iron-based superconductors are discussed.
We report neutron diffraction measurements of the magnetic structures in two pyrochlore iridates, Yb2Ir2O7 and Lu2Ir2O7. Both samples exhibit the all-in-all-out magnetic structure on the Ir4+ sites below TN~ 150,K, with a low temperature moment of around 0.45 muB/Ir. Below 2,K, the Yb moments in Yb2Ir2O7 begin to order ferromagnetically. However, even at 40 mK the ordered moment is only 0.57(3)muB/Yb, well below the saturated moment of the ground state doublet of Yb3+ (1.9 muB/Yb), deduced from magnetization measurements and from a refined model of the crystal field environment, and also significantly smaller than the ordered moment of Yb in Yb2Ti2O7 (0.9 muB/Yb). A mean-field analysis shows that the reduced moment on Yb is a consequence of enhanced phase competition caused by coupling to the all-in-all-out magnetic order on the Ir sublattice.
We consider the scaling behavior of thermodynamic quantities in the one-dimensional transverse-field Ising model near its quantum critical point (QCP). Our study has been motivated by the question about the thermodynamical signatures of this paradigmatic quantum critical system and, more generally, by the issue of how quantum criticality accumulates entropy. We find that the crossovers in the phase diagram of temperature and (the non-thermal control parameter) transverse field obey a general scaling ansatz, and so does the critical scaling behavior of the specific heat and magnetic expansion coefficient. Furthermore, the Gr{u}neisen ratio diverges in a power-law way when the QCP is accessed as a function of the transverse field at zero temperature, which follows the prediction of quantum critical scaling. However, at the critical field, upon decreasing the temperature, the Gruneisen ratio approaches a constant instead of showing the expected divergence. We are able to understand this unusual result in terms of a peculiar form of the quantum critical scaling function for the free energy; the contribution to the Gruneisen ratio vanishes at the linear order in a suitable Taylor expansion of the scaling function. In spite of this special form of the scaling function, we show that the entropy is still maximized near the QCP, as expected from the general scaling argument. Our results establish the telltale thermodynamic signature of a transverse-field Ising chain, and will thus facilitate the experimental identification of this model quantum-critical system in real materials.
In frustrated magnetic systems with competing interactions fluctuations can lift the residual accidental degeneracy. We argue that the state selection may have different outcomes for quantum and thermal order by disorder. As an example, we consider the semiclassical Heisenberg fcc antiferromagnet with only the nearest-neighbor interactions. Zero-point oscillations select the type 3 collinear antiferromagnetic state at T=0. Thermal fluctuations favor instead the type 1 antiferromagnetic structure. The opposite tendencies result in a finite-temperature transition between the two collinear states. Competition between effects of quantum and thermal order by disorder is a general phenomenon and is also realized in the J1-J2 square-lattice antiferromagnet at the critical point J2 = 0.5 J1.
For a system near a quantum critical point (QCP), above its lower critical dimension $d_L$, there is in general a critical line of second order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, $d_{eff}=d+z$ ($d$ is the Euclidean dimension of the system and $z$ the dynamic quantum critical exponent) is above its upper critical dimension $d_C$, there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation $psi= u z$ between the shift exponent $psi$ of the critical line and the crossover exponent $ u z$, for $d+z>d_C$ by a textit{dangerous irrelevant interaction}. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
