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Register a new userCollective modes in a quantum solid
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We provide a theoretical explanation for the optical modes observed in inelastic neutron scattering (INS) on the bcc solid phase of helium 4 [T. Markovich, E. Polturak, J. Bossy, and E. Farhi, Phys. Rev. Lett. 88, 195301 (2002)]. We argue that these excitations are amplitude (Higgs) modes associated with fluctuations of the crystal order parameter within the unit cell. We present an analysis of the modes based on an effective Ginzburg-Landau model, classify them according to their symmetry properties, and compute their signature in INS experiments. In addition, we calculate the dynamical structure factor by means of an ab intio quantum Monte Carlo simulation and find a finite frequency excitation at zero relative momentum.
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We study properties of thermal transport and quantum many-body chaos in a lattice model with $Ntoinfty$ oscillators per site, coupled by strong nonlinear terms. We first consider a model with only optical phonons. We find that the thermal diffusivity $D_{rm th}$ and chaos diffusivity $D_L$ (defined as $D_L = v_B^2/ lambda_L$, where $v_B$ and $lambda_L$ are the butterfly velocity and the scrambling rate, respectively) satisfy $D_{rm th} approx gamma D_L$ with $gammagtrsim 1$. At intermediate temperatures, the model exhibits a ``quantum phonon fluid regime, where both diffusivities satisfy $D^{-1} propto T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $hbar/k_B T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstones theorem. As a result, for $d=1,2$, we find that $D_{rm th}/D_Lto infty$, while for $d=3$, $D_{rm th}$ and $D_{L}$ remain comparable.
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.
We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focussing on the nearest-neighbour pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a U(1) emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.
Being the simplest element with just one electron and proton the electronic structure of the Hydrogen atom is known exactly. However, this does not hold for the complex interplay between them in a solid and in particular not at high pressure that is known to alter the crystal as well as the electronic structure. Back in 1935 Wigner and Huntington predicted that at very high pressure solid molecular hydrogen would dissociate and form an atomic solid that is metallic. In spite of intense research efforts the experimental realization, as well as the theoretical determination of the crystal structure has remained elusive. Here we present a computational study showing that the distorted hexagonal P6$_3$/m structure is the most likely candidate for Phase III of solid hydrogen. We find that the pairing structure is very persistent and insulating over the whole pressure range, which suggests that metallization due to dissociation may precede eventual bandgap closure. Due to the fact that this not only resolve one of major disagreement between theory and experiment, but also excludes the conjectured existence of phonon-driven superconductivity in solid molecular hydrogen, our results involve a complete revision of the zero-temperature phase diagram of Phase III.
We consider collective excitations of a Fermi liquid. For each value of the angular momentum $l$, we study the evolution of longitudinal and transverse collective modes in the charge (c) and spin (s) channels with the Landau parameter $F_l^{c(s)}$, starting from positive $F_l^{c(s)}$ and all the way to the Pomeranchuk transition at $F_l^{c(s)} = -1$. In each case, we identify a critical zero-sound mode, whose velocity vanishes at the Pomeranchuk instability. For $F_l^{c(s)} < -1$, this mode is located in the upper frequency half-plane, which signals an instability of the ground state. In a clean Fermi liquid the critical mode may be either purely relaxational or almost propagating, depending on the parity of $l$ and on whether the response function is longitudinal or transverse. These differences lead to qualitatively different types of time evolution of the order parameter following an initial perturbation. A special situation occurs for the $l = 1$ order parameter that coincides with the spin or charge current. In this case the residue of the critical mode vanishes at the Pomeranchuk transition. However, the critical mode can be identified at any distance from the transition, and is still located in the upper frequency half-plane for $F_1^{c(s)} < -1$. The only peculiarity of the charge/spin current order parameter is that its time evolution occurs on longer scales than for other order parameters. We also analyze collective modes away from the critical point, and find that the modes evolve with $F_l^{c(s)}$ on a multi-sheet Riemann surface. For certain intervals of $F_l^{c(s)}$, the modes either move to an unphysical Riemann sheet or stay on the physical sheet but away from the real frequency axis. In that case, the modes do not give rise to peaks in the imaginary parts of the corresponding susceptiblities.
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