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arXiv:1402.0875 · Physical Review B

Quantum quenches and competing orders

Wenbo Fu, Ling-Yan Hung, Subir Sachdev A

Published Jul 10, 2014• 24 citations
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Abstract

We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, $(\mathbit{k},\ensuremath{-}\mathbit{k})$, in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear $\ensuremath{\sigma}$ model of competing orders in the underdoped cuprates [Hayward et al., Science 343, 1336 (2014)]. We obtain results, in the large $N$ limit of a $O(N)$ model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.

DOI
10.1103/physrevb.90.024506

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We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and ddd-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, (\mathbitk,\ensuremath−\mathbitk)(\mathbit{k},\ensuremath{-}\mathbit{k})(\mathbitk,\ensuremath−\mathbitk), in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear \ensuremathσ\ensuremath{\sigma}\ensuremathσ model of competing orders in the underdoped cuprates [Hayward et al., Science 343, 1336 (2014)]. We obtain results, in the large NNN limit of a O(N)O(N)O(N) model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.
We study the non-equlibrium dynamics of an electronic model of competing bond density wave order and ddd-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, (k,−k)(\boldsymbol{k}, -\boldsymbol{k})(k,−k), in the Brillouin zone. We compare the results of numerical studies of our model with recent picosecond optical experiments.
We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large NNN limit of a O(NNN) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.
We use a number of large-N limits to explore the competition between ground states of square lattice doped antiferromagnets which break electromagnetic U(1),U(1),U(1), time-reversal, or square lattice space-group symmetries. Among the states we find are d-, ${(s}^{*}+id)\ensuremath{-},$ and ${(d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}})$-wave superconductors, Wigner crystals, Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux states), and states with spin-Peierls and bond-centered charge stripe order. In the vicinity of second-order quantum phase transitions between the states, we go beyond the large-N limit by identifying the universal quantum field theories for the critical points, and computing the finite temperature, quantum critical damping of fermion spectral functions. We identify candidate critical points for the recently observed quantum critical behavior in photoemission experiments on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}\mathrm{}\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ by Valla et al. [Science 285, 2110 (1999)]. These involve onset of a charge-density wave, or of broken time-reversal symmetry with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$ or s∗+id{s}^{*}+ids∗+id pairing, in a d-wave superconductor. It is not required (although it is allowed) that the stable state in the doped cuprates be anything other than the d-wave superconductor---the other states need only be stable nearby in parameter space. At finite temperatures, fluctuations associated with these nearby states lead to the observed fermion damping in the vicinity of the nodal points in the Brillouin zone. The cases with broken time-reversal symmetry are appealing because the order parameter is not required to satisfy any special commensurability conditions. The observed absence of inelastic damping of quasiparticles with momenta $(\ensuremath{\pi},k),$ $(k,\ensuremath{\pi})$ (with $0<~k<~\ensuremath{\pi})$ also appears very naturally for the case of fluctuations to ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$ order.
Engineering quantum phases using light is a novel route to designing functional materials, where lightinduced superconductivity is a successful example.Although this phenomenon has been realized experimentally, especially for the high-T c cuprates, the underlying mechanism remains mysterious.Using the recently developed variational non-Gaussian exact diagonalization method, we investigate a particular type of photoenhanced superconductivity by suppressing a competing charge order in a strongly correlated electron-electron and electron-phonon system.We find that the d-wave superconductivity pairing correlation can be enhanced by a pulsed laser, consistent with recent experiments based on gap characterizations.However, we also find that the pairing correlation length is heavily suppressed by the pump pulse, indicating that light-enhanced superconductivity may be of fluctuating nature.Our findings also imply a general behavior of nonequilibrium states with competing orders, beyond the description of a mean-field framework.
We study the charge-density-wave order and its competition with superconductivity in the one-band Hubbard model for high-Tc{T}_{c}Tc​ superconducting cuprates. We use cluster dynamical mean field theory at T=0T=0T=0. The one-band Hubbard model contains only copper atoms, and a physical charge-density wave with charge excesses located on the oxygen atoms manifests itself as a bond-density wave (BDW) within this context. It arises purely out of local correlation effects and also leads to an ${s}^{\ensuremath{'}}$-wave pair-density wave in the presence of ddd-wave superconductivity. The ddd-wave BDW is suppressed on increasing UUU and is favored on increasing the magnitude of the second-neighbor hopping ${t}^{\ensuremath{'}}$. Further, the ddd-wave BDW order is weakened when in competition with superconductivity, as seen in experiments. Additionally, it behaves quite differently on varying UUU in the superconducting state compared to the normal state.
Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the ``linear-response assumption'' is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.