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Register a new userHiggs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
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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 $Ngeq 3$.
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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.
Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu$-$Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics, is prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low dimensions. Especially, observation of a Higgs amplitude mode in two dimensions is an outstanding experimental challenge. Here, using the inelastic neutron scattering and applying the bond-operator theory, we directly and unambiguously identify the Higgs amplitude mode in a two-dimensional S=1/2 quantum antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$ near a quantum critical point in two dimensions. Owing to an anisotropic energy gap, it kinematically prevents such decay and the Higgs amplitude mode acquires an infinite lifetime.
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 $T lesssim 0.1 J$.
We consider a 3-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter g. Starting from the magnetically ordered phase, the N{e}el temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behaviour near the QCP. We compare our results with available data for TlCuCl_3
The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, 3He p-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here we report the first observation of this mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence from the condensate, we observe weak but distinct photoluminescence at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode. These energies, as well as the overall structure of the photoluminescence spectra, are in good agreement with our theoretical analysis.
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