Using Nonequilibrium Dynamics to Probe Competing Orders in a Mott-Peierls System

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softening due to a stronger coupling near $k_F$. This behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.

Figure 1

(a) Diagram showing the photoexcitation process from the Peierls ground state (top panel). This process is realized by a coherent, uniform removal of an electron with zero net momentum (middle panel). The consequence is projection of the ground state into a Hilbert space with $N-1$ particles and a reduced charge modulation (bottom panel). (b) Phonon occupations and (c) local moment at various $\lambda$ and $u$. In both figures, the dashed line denotes the antiadiabatic limit phase boundary ($u_{\mathrm{eff}}=0$) and the solid line denotes the boundary of the Peierls phase in terms of ground state degeneracy. The triangles indicate the positions of correspondingly colored lines of Figs. 2 and 2.

Figure 2

(a) False color plots of the spin density $\mathrm{\Delta }S(q,t)$ and charge density $\mathrm{\Delta }N(q,t)$ dynamics for $u=7.8$ and $\lambda =4$ (strong-coupling regime) after photoexcitation at the $\mathrm{\Gamma }$ point. (b),(c) Evolution of (b) $N(\pi ,t)$ and (c) $S(\pi ,t)$ with various parameters (shown in the inset). (d) The suppression of CDW ${\eta }_{\mathrm{ch}}$ (solid markers) and enhancement of AFM ${\zeta }_{\mathrm{sp}}$ (open markers) in the Peierls phase (shown in the inset). (e) The comparison of dominant energy scales in $N(\pi ,t)$ and $S(\pi ,t)$ dynamics (solid circles) and the renormalized phonon frequencies (open circles) evaluated via the equilibrium spectral function $A(k,\omega )$, as indicated in the inset. The frequencies are compared along the $u$ axis with $\lambda =3$, 4, and 5. The error bars denote the corresponding half width at full maximum in the Fourier spectrum due to a finite time window.

Figure 3

The Fourier spectrum of $N(\pi ,t)$ for photoexcitation with different fermion momentum, calculated along a path through the phase diagram indicated by the colored arrow. (a)–(e) follow the path with fixed $u=5$ and increasing $\lambda$; while (e)–(i) follow the path with fixed $\lambda =4$ and increasing $u$. Among them, (e) is deep in the Peierls phase; (b) and (h) are close to the phase boundary; (a) and (i) are outside the phase. $k_F$ is denoted by the dashed lines. The inset reflects the path in parameter space.