Perturbative calculation of critical exponents for the Bose–Hubbard model

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose–Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a ₆ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose–Hubbard model, deviate by less than 1 % from the best known estimates computed so far for the three-dimensional XY universality class.     

An apparent Landau-type second order transition in the spinel CdIn2S4

Experimental evidence is given of a second order transition in the spinel CdIn₂S₄. The specific heatc _p shows a step at the transition temperature (T _c=403°K), the thermal expansion coefficientα remains unaffected. An analysis yields a critical region of this transition considerably narrower (5°K) than expected from the critical regions of transitions of a similar type (quartz: 160°K,β-brass: 250°K) and therefore the critical region has not been observed experimentally, i.e. the transition appears to follow Landau’s theory. Landau’s group theoretical analysis of second order transitions in crystals leads to a model for the transition in CdIn₂S₄ on the atomic scale. If the temperature is decreased below the critical temperature a 1:1 ordering occurs between Cd and In on the tetrahedral sites. With this model the gross features of this transition can be qualitatively understood: The unaffected thermal expansion and the long relaxation times for the establishment of equilibrium approachingT _c. Also the narrow critical region can be explained in terms of a large correlation length in CdIn₂S₄. Finally it is shown that a generalized formulation of the thermodynamic part of Landau’s theory correlates thermodynamic quantities far above and far below the critical temperature, as illustrated for CdIn₂S₄. This generalization allows also a more satisfactory determination of the critical region.     

Metal-insulator transition induced by the magnetic field in n-type GaSb

The metal-insulator (MI) transition induced by a magnetic field was evidenced for the first time in compensated n-type GaSb layers grown by molecular beam epitaxy. The free electron densities were in the low 10¹⁶ cm⁻³ range or even slightly lower, so that the zero-field 3D electron gas was degenerate and, at the B_MI magnetic field of the MI transition, it populates only the spin-split 0⁽⁺⁾ Landau level (extreme quantum limit). On the metallic side of the MI transition a T^1/3 dependence of the conductivity was assumed to fit the low-T data and to estimate the B_MI value, which resulted of 9.1 T in the purest sample. The MI transition manifests in a strong increase of the diagonal resistivity with the magnetic field, but not of the Hall coefficient, suggesting that the apparent electron density is practically constant, whereas the mobility varies strongly. The evidence of a maximum in the temperature dependence of the Hall coefficient has been explained through a two channels transport mechanism involving localized and extended states.     

Anomalous asymmetry of magnetoresistance in NbSe3 single crystals

A pronounced asymmetry of magnetoresistance with respect to the magnetic field direction is observed for NbSe₃ crystals placed in a magnetic field perpendicular to their conducting planes. It is shown that the effect persists in a wide temperature range and manifests itself starting from a certain magnetic induction value B ₀, which at T = 4.2 K corresponds to the transition to the quantum limit, i.e., to the state where the Landau level splitting exceeds the temperature.     

Critical magnetic field ratio of anisotropic magnetic superconductors

The upper critical field, the lower critical field and the critical magnetic field ratio of anisotropic magnetic superconductors are calculated by Ginzburg–Landau theory analytically. The effect of the Ginzburg–Landau parameter (κ₀), magnetic susceptibility (χ) and magnetic-to-anisotropic parameter ratio (θ) on the critical field ratio are considered. We find that the value of critical field ratio increases with increasing κ₀ and θ, and decreases with increasing χ. The highest and the lowest value of critical field ratio is found in the diamagnetic superconductors and the ferromagnetic superconductors, respectively.     

Excitonic effects in low density electron-hole plasma in InGaAs/InP quantum wells under magnetic field

The magnetic-field and excitation-density dependencies of the photoluminescence of undoped In_0.53Ga_0.47As/InP single quantum well structures have been investigated. A clear transition from excitonic to free-carrier-like recombination has been observed while changing the electron-hole density from 10¹⁰ to 10¹² cm⁻². Excitonic correlations are found to be well pronounced for carriers at the upper partly occupied Landau levels.     

On the nature of the phase transition in the KDP systems

Using the Landau theory of phase transitions it has been shown that for a second order phase transition Ω/k_BT_c ? 0.01. and its isomorphs 4Ω/J¹ ? 1 and for a first order transition Ω/k_BT_c ? 0.01.     

Interrelation of antiferrodistortive and ferroelectric phase transitions in Sr1−xAxTiO3 (A=Ba, Pb)

A dielectric and ultrasonic velocity study of antiferrodistortive and ferroelectric phase transitions in Sr_1−xA_xTiO₃ (A=Ba, Pb) is reported. It is shown that both phase transitions co-exist at x<0.03 but at the higher concentration the ferroelectric phase transition entirely suppresses the antiferrodistortive phase transition. The experimentally obtained phase diagrams are discussed in the framework of the Landau phenomenological theory.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Magnetic phase diagram of UCoAl

Temperature T and pressure P dependences of the Landau coefficients for UCoAl are discussed by taking into account the magneto-volume effects and anisotropic spin fluctuations based on the Landau–Ginzburg theory. The P-dependence of the mean square amplitude of spin fluctuations is also discussed. A magnetic phase diagram is obtained with the parameters estimated from the observed magnetization curves under high pressures. The P-dependences of the characteristic temperatures T₀ and T_max, where the metamagnetic transition disappears and the susceptibility reaches a maximum, are estimated and compared with the observed results.     

General properties of a magnetic-field-induced landau Fermi liquid in high-temperature superconductors and heavy fermion metals

It has been shown that the magnetic-field-induced transition from a non-Fermi-liquid state to a Fermi liquid state in the Tl₂Ba₂CuO_{6 + x} high-temperature superconductor is similar to a transition observed in heavy fermion metals. This behavior is explained in the theory of the Fermi condensate quantum-phase transition implying the existence of Landau quasiparticles. The Fermi condensate quantum-phase transition can be considered as a universal cause of the strongly correlated behavior observed in various metals and liquids such as high-temperature superconductors, heavy fermion metals, and two-dimensional Fermi systems.     

The pressure effect on the CDW-transition temperatures in 1T-TaS2

The pressure dependence of the two CDW transition temperatures (T_d1? 350 K and T_d2 ～ 190 K) in 1T-TaS₂ has been investigated by measuring the resistivity up to 5 kbar. It is found that the thermal hysteresis of the phase transition at T_d2 is very sensitive to the pressure and is interpreted by the phenomenological Landau theory including cubic term.     

Static and dynamical elastic behaviour of squaric acid around its phase transition

Ultrasonic velocity measurements could be performed on a good quality single crystal of squaric acid close to its transition temperature around 373 K. The behaviour of the stiffness componentsc ₃₃ andc ₄₄ clearly demonstrates a first-order transition. The temperature variation ofc ₁₁ andc ₆₆ can be fitted to a formula obtained from the Landau theory and assuming a strictive-type coupling between order parameter and strain. From attenuation measurements characteristic times for the order-parameter dynamics can be estimated, ranging from 10^?11 to several 10^?10s in a temperature range of about 12 K on either side of the transition.     

First order β, γ phase transition in NH4Br

The course of the order parameter around the β, γ phase transition (235 K) in the NH₄Br has been closely observed by means of linear optical birefringence. The experimental data were fitted in the critical region T > 0.9T₀ by the Landau theory and a simple power law. Both relations reveal a first order transition, with the jump height in the birefringence amounting to Δn(T₀)/?Δn(120 K) = 0.145.     

Dielectric study of the ferroelectric phase transition of KH2PO4

We report high precision measurements of the dielectric constant of Potassium Dihydrogen Phosphate as a function of temperature and electric field. Landau model parameters are evaluated and the biasing field E_c which drives the transition second order is determined.     

Symmetry breaking term effects on explosive localized solitons

We study the influence of an analog of self–steepening (SST), which is a term breaking the T →?T symmetry, on explosive localized solutions for the cubic–quintic complex Ginzburg–Landau equation in the anomalous dispersion regime. We find that while this explosive behavior occurs for a wide range of the parameter s, characterizing SST, the mean distance between explosions diverges close to a critical value s _c . After this value the explosive solution becomes a fixed shape soliton that moves at constant speed. The transition between explosive and regular behavior is characterized by a transcritical bifurcation controlled by the SST parameter. We also proposed a mechanism which explains and predicts the mean distance between explosions as a function of s. We are glad to dedicate this article to Professor Helmut R. Brand on occasion of his 60^th birthday.     

Zener tunneling between Landau levels in a double quantum well at high filling factors

Differential resistance r _xx in a double GaAs quantum well with two occupied size-quantization subbands has been studied at a temperature of 4.2 K in magnetic fields B < 2 T. The oscillations of r _xx with a period in the inverse magnetic field determined by the value of a dc bias current I _dc have been discovered in the electron system under investigation at high filling factors in the presence of I _dc. The amplitude of magneto-intersubband oscillations has been shown to increase in the r _xx oscillation maxima, while the oscillation reversal has been observed in the minima. The discovered oscillations have been shown to be due to Zener tunneling of electrons between Landau levels tilted by a Hall electric field. The experimental data are qualitatively explained by the effect of intersubband transitions on the I _dc-dependent component of the electron distribution function.     

The influence of magnetoelastic interaction on structural phase transitions in cubic ferromagnetics

In the framework of the Landau theory of phase transitions, the influence of the magnetoelastic interaction on structural transitions in cubic ferromagnetics with a positive first magnetic anisotropy constant is analyzed. It is shown that structural transitions are not accompanied by a reorientation of magnetization in this case. The phase diagrams of such ferromagnetics either contain a termination point of the structural transition or a critical point in which the first-order transition is replaced by a second-order one. Magnetoelastic interaction also leads to the appearance of an interval of the ferromagnetic parameters in which a coupled first-order structural-magnetic transition exists. The phase T?x diagram for Heusler Ni_2+x Mn_1?x Ga alloys is calculated, which is in good agreement with the experimental phase diagram of these alloys.     

Magnetic sub-band structure of HgTe under uniaxial stress

The magnetic sub-band structure of HgTe is calculated for the strain-splitting Γ₈ bands, and the lowest Landau levels of the conduction and valence bands at k_H = 0 are shown to cross each other as the magnetic field is increased. It is demonstrated that the crossing means the band inversion for the case of the compressional stress and the semimetal—semiconductor transition for the case of the tensile stress.     

Effect of chiral solute on the smectic a to C phase transition of second order

The Landau theory is applied to explain the helicoidal effect of a chiral solute on an ordinary smectic C state below a smectic A-C phase transition of second order. It is shown that T_c increases with the concentration c of the solute, for small c. We suggest that a simultaneous application of electric and magnetic fields perpendicular to the smectic layers might, in some cases, also make the C phase helicoidal.