Breakdown of adiabaticity in topological quantum liquids

TL;DR

This work addresses adiabaticity in strongly long-range, fermionic topological fluids by analyzing a decorated Kitaev chain with infinite-range couplings and a slow quasi-static ramp across the critical point. Using an analytically tractable momentum-space formulation and Bogoliubov transformation, it shows that strong long-range interactions enforce mean-field-like adiabatic scaling $n_{ m exc} \propto δ^{2}$ for critical quenches, yet can produce an extensive defect density when the ramp ends at the edge of the topological phase. A central result is the emergence of a non-adiabatic dynamical phase at $\lambda_f=0$, where high-energy modes become highly degenerate and Landau-Zener tunneling is suppressed, causing $p_n$ to approach a $δ$-independent constant in the thermodynamic limit and yielding $N_{ m exc} \propto N$. These findings reveal a mechanism by which strong long-range interactions break adiabaticity in fermionic topological matter and imply fundamental limits for adiabatic state preparation and quantum annealing in such systems, with implications extending beyond the $\alpha=0$ limit to all $\alpha<d$.

Abstract

We study the temporal behavior of topological quantum fluids with strong long-range couplings under slow external perturbations, whose rate $δ$ approaches the quasi-static limit $δ\to 0$. As expected, due to strong long-range interactions, the system lies in the mean-field universality and the density of defects for drives across the quantum critical point is adiabatic $n_{\rm exc}\propto δ^{2}$. However, if the drive is instead terminated precisely at the edge of the topological non-trivial phase, the number of generated excitations becomes extensive $n_{\rm exc}\propto O(1)$. This result fundamentally breaks the established universal behavior observed in local topological quantum fluids and demonstrates a novel mechanism for the breakdown of adiabaticity in fermionic systems with strong long-range interactions.

Figures (3)

• Figure 1: The hopping (blue) and pairing (red) couplings of the strong long-range Kitaev chain. Panel a) illustrates both the single particle hopping terms ($j_{r}\hat{a}^{\dagger}_{i+r}\hat{a}_{i}$), represented by the blue lines, as well as the pairing terms ($\Delta \hat{a}^{\dagger}_{i+r}\hat{a}^{\dagger}_{i} + \text{h.c.}$) depicted by the red ones. The hopping term allows particles (grey shaded dots) to hop in between sites while the pairings allows for processes where the particles are created or annihilated in pairs, increasing or decreasing the total number of fermions $N_f$ by two ($N_f\to N_f \pm2$). Panel b) represents the result of the Fourier series for a finite system of size $N=2^{10}$, $\alpha=2/\pi$ and $\lambda=1$. The dashed lines are the asymptotic expressions obtained in the thermodynamic limit (see Eq. \ref{['kin_en']} and Eq. \ref{['pair_en']})
• Figure 2: The temperature profiles in the three out-of-equilibrium phases—positive temperature (blue), negative temperature (red), and infinite temperature (green)—are shown as functions of momentum $k$ in the short-range case ($\alpha \gtrsim 11$, left panel) and as functions of mode index $n$ in the strong long-range case ($\alpha \simeq 0.5$, center panel). The fluctuations observed in the strong long-range case vanish in the thermodynamic limit. The right panel shows the increase of the negative temperature region as the endpoint of the quench goes deeper in the broken phase $\lambda_{f}\to 0$. All lines have been computed for $N=1024$ and $\delta=1$
• Figure 3: Behavior of $p_{n}$ as a function of $\delta$ for the effective large-$N$ model in Eq. \ref{['largeNeffectivemodel']} with $t_{\text{f}}=0$. The behavior of different $n$ is shown and in all cases $\alpha=1/e$ as well as the theoretical prediction from Eq.\ref{['eq:thermodynamiclimitfirst']}. We can observe how, as we approach the high energy modes ($n\approx N$) the excitation probability exactly corresponds to the constant value predicted by Eq.\ref{['eq:thermodynamiclimitfirst']}