Thermodynamics in the vicinity of a relativistic quantum critical point in2+1dimensions

Abstract

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))F(N)(Δ/T), where c is the velocity of the excitations at the QCP and |Δ| 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 F(N). For small values of N (N</~10) we find that F(N)(x) is nonmonotonic in the quantum critical regime (|x|</~1) with a maximum near x=0. The large-N approach-if properly interpreted-is a good approximation both in the renormalized classical (x</~-1) and quantum disordered (x>/~1) regimes, but fails to describe the nonmonotonic behavior of F(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 T(BKT)/ρ(s)(0) is very close to π/2, implying that the stiffness ρ(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ρ(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.

Higgs amplitude mode in the vicinity of a(2+1)-dimensional quantum critical point: A nonperturbative renormalization-group approach

“…II A). For small values of N , we find significant deviations wrt previous NPRG results [41]. The value for N = 2 is now much closer to the MC estimate of Ref.…”

“…Also shown are the previous NPRG results obtained from a derivative expansion of the effective action[41] (NPRG DE) and from Monte Carlo simulations[15] (MC). The exact result in the limit N → ∞ is 1/4π 0.0796.…”

Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides

“…Our goal is to investigate general properties, including issues of universality and the order of the phase transitions of the present setting, which contains two order parameters possibly competing or coexisting. We note that the well-known large-N approach has proved fruitful for many problems in statistical physics [26,27].…”

“…Since it is important to establish the nature of quantum criticality in the absence of superconductivity [14,19,20], we will focus on the transitions in the normal state and will not consider the effect of superconductivity [25]. Using a large-N approach [26,27], we demonstrate that the AF and Ising-nematic transitions are concurrent at zero temperature both for the case of a square lattice and in the presence of interlayer coupling. Moreover, both transitions are only weakly first order in accordance with the marginal nature of the relevant coupling, with jumps in both order parameters that are very small, which implies a large dynamical range for quantum criticality.…”

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

“…In the LPA , we expect 30 This result should be valid for |p| smaller than the Ginzburg momentum scale p G ∼ u 0 /24π. 31 Thus the anomalous dimension η can be retrieved from the momentum dependence of Z k (p).…”