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Register a new userThermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
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We study the thermodynamics of the relativistic quantum O($N$) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form $P(T)=P(0)+N(T^3/c^2)calF_N(Delta/T)$ where $c$ is the velocity of the excitations at the QCP and $Delta$ is a characteristic zero-temperature energy scale. Using both a large-$N$ approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function $calF_N$. For small values of $N$ ($Nlesssim 10$) we find that $calF_N(x)$ is nonmonotonous in the quantum critical regime ($|x|lesssim 1$) with a maximum near $x=0$. The large-$N$ approach -- if properly interpreted -- is a good approximation both in the renormalized classical ($xlesssim -1$) and quantum disordered ($xgtrsim 1$) regimes, but fails to describe the nonmonotonous behavior of $calF_N$ in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio $Tkt/rho_s(0)$ is very close to $pi/2$, implying that the stiffness $rho_s(Tkt^-)$ at the transition is only slightly reduced with respect to the zero-temperature stiffness $rho_s(0)$. Finally, we briefly discuss the experimental determination of the universal function $calF_2$ from the pressure of a Bose gas in an optical lattice near the superfluid--Mott-insulator transition.
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We study the Higgs amplitude mode in the relativistic quantum O($N$) model in two space dimensions. Using the nonperturbative renormalization group we compute the O($N$)-invariant scalar susceptibility in the vicinity of the zero-temperature quantum critical point. In the zero-temperature ordered phase, we find a well defined Higgs resonance for $N=2$ with universal properties in agreement with quantum Monte Carlo simulations. The resonance persists at finite temperature below the Berezinskii-Kosterlitz-Thouless transition temperature. In the zero-temperature disordered phase, we find a maximum in the spectral function which is however not related to a putative Higgs resonance. Furthermore we show that the resonance is strongly suppressed for $Ngeq 3$.
We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wavefunction renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $mu$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization group calculations for thermodynamic observables at $mu =0$ to finite values of $mu$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, the susceptibility, and the correlation length of the two-dimensional spin-$1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $mu leq 0$ rather accurately up to relatively high temperatures $T lesssim 0.1 J$.
Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4.
The angular, temperature and magnetic field dependences of Hall resistance roH for the rare-earth dodecaboride solid solutions Tm1-xYbxB12 have been studied in a wide vicinity of the quantum critical point (QCP) xC~0.3. The measurements performed in the temperature range 1.9-300 K on high quality single crystals allowed to find out for the first time in these fcc compounds both an appearance of the second harmonic contribution in ro2H at QCP and its enhancement under the Tm to ytterbium substitution and/or with increase of external magnetic field. When the Yb concentration x increases a negative maximum of a significant amplitude was shown to appear on the temperature dependences of Hall coefficient RH(T) for the Tm1-xYbxB12 compounds. Moreover, a complicated activation type behavior of the Hall coefficient is observed at intermediate temperatures for x>0.5 with activation energies Eg~200K and Ea~55-75K in combination with the sign inversion of RH(T) at low temperatures in the coherent regime. The density of states renormalization effects are analyzed within the variation of Yb concentration and the features of the charge transport in various regimes (charge gap formation, intra-gap manybody resonance and coherent regime) are discussed in detail in Tm1-xYbxB12 solid solutions.
The quantum critical behavior of the 2+1 dimensional Gross--Neveu model in the vicinity of its zero temperature critical point is considered. The model is known to be renormalisable in the large $N$ limit, which offers the possibility to obtain expressions for various thermodynamic functions in closed form. We have used the concept of finite--size scaling to extract information about the leading temperature behavior of the free energy and the mass term, defined by the fermionic condensate and determined the crossover lines in the coupling ($g$) -- temperature ($T$) plane. These are given by $Tsim|g-g_c|$, where $g_c$ denotes the critical coupling at zero temperature. According to our analysis no spontaneous symmetry breaking survives at finite temperature. We have found that the leading temperature behavior of the fermionic condensate is proportional to the temperature with the critical amplitude $frac{sqrt{5}}3pi$. The scaling function of the singular part of the free energy is found to exhibit a maximum at $frac{ln2}{2pi}$ corresponding to one of the crossover lines. The critical amplitude of the singular part of the free energy is given by the universal number $frac13[frac1{2pi}zeta(3)-mathrm{Cl}_2(frac{pi}3)]=-0.274543...$, where $zeta(z)$ and $mathrm{Cl}_2(z)$ are the Riemann zeta and Clausens functions, respectively. Interpreted in terms the thermodynamic Casimir effect, this result implies an attractive Casimir force. This study is expected to be useful in shedding light on a broader class of four fermionic models.
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