Cluster Ising quantum batteries can mimic super-extensive charging power

Abstract

Quantum batteries, miniaturized devices able to store and release energy on demand, are promising both because their intrinsic energy and time scales can match those of other quantum technologies and due to the intriguing possibility of achieving super-extensive charging power. While this enhanced scaling is known to appear in several settings, it is generally believed to be forbidden in Wigner-Jordan integrable spin chains charged via quantum-quench protocols. Here, we show that an extended cluster-Ising model, despite belonging to the above category, exhibits super-extensive charging power over wide ranges of system sizes, reaching up to a thousand spins, in proper parameter regimes. This remarkable anomalous scaling is due to a corresponding super-extensive growth of the stored energy, implying that it occurs at large but finite size and cannot persist in the thermodynamic limit. This phenomenon appears robust against finite-temperature effects.

Figures (10)

• Figure 1: (Color online) Stored energies per spin $E_{1}(\tau)$ (a) and $E_{2}(\tau)$ (b) as a function of the charging time $\tau$ and at zero temperate for different values of $N$ (ranging from $N=169$ to $N=324$ for (a) and from $N=36$ to $N=196$ for (b)) and at fixed $n=15$. Averaged charging power per spin $P_{1}(\tau)$ (c) and $P_{2}(\tau)$ (d) as a function of the charging time $\tau$ and at zero temperature for different values of $N$ (ranging from $N=169$ to $N=324$ for (c) and from $N=36$ to $N=196$ for (d)) and at fixed $n=15$.
• Figure 2: (Color online) Best fit of $P^{M}_{1}$ (a) and $P^{M}_{2}$ (b) extracted from Fig.\ref{['fig1']} (c) and (d) in the form $P^{M}_{1/2}=a_{1/2} N^{\alpha_{1/2}}$. The blue curves correspond to ($a_{1}\approx 0.00019$, $\alpha_{1}\approx 0.8327$) and ($a_{2}\approx 0.001$, $\alpha_{2}\approx 0.8933$) respectively.
• Figure 3: (Color online) Best fit of $P^{M}_{1}$ (left panels) and $P^{M}_{2}$ (right panels) in the form $P^{M}_{1/2}=a_{1/2} N^{\alpha_{1/2}}$ for: the case $n=N^{\frac{1}{2}}$ (a-b), the blue curves corresponding to ($a_{1}\approx 0.0013$, $\alpha_{1}\approx 0.4766$) and ($a_{2}\approx 0.0084$, $\alpha_{2}\approx 0.4989$) respectively; $n=N^{\frac{2}{3}}$ (c-d), the blue curves corresponding to ($a_{1}\approx 0.0016$, $\alpha_{1}\approx 0.3015$) and ($a_{2}\approx 0.0083$, $\alpha_{2}\approx 0.3561$) respectively.
• Figure 4: (Color online) Best fit of $P^{M}_{1}$ (left panels) and $P^{M}_{2}$ (right panels) in the form $P^{M}_{1/2}=a_{1/2} N^{\alpha_{1/2}}$ for: fixed  $n=15$ (a-b), the blue curves corresponding to ($a_{1}\approx 0.00015$, $\alpha_{1}\approx 0.6943$) and ($a_{2}\approx 0.00036$, $\alpha_{2}\approx 0.8595$) respectively; the case  $n=N^{\frac{1}{2}}$ (c-d), the blue curves corresponding to ($a_{1}\approx 0.00064$, $\alpha_{1}\approx 0.4275$) and ($a_{2}\approx 0.0035$, $\alpha_{2}\approx 0.4326$) respectively; the case  $n=N^{\frac{2}{3}}$ (e-f), the blue curves corresponding to ($a_{1}\approx 0.00076$, $\alpha_{1}\approx 0.2699$) and ($a_{2}\approx 0.0029$, $\alpha_{2}\approx 0.3272$) respectively. All the plots are done at the same fixed inverse temperature $\beta = 1$.
• Figure 5: (Color online) Behavior of $P^{M}_{1}$ for $n=N/2$ (a) and $P^{M}_{2}$ for $n=N^{\frac{1}{3}}$ (b) at zero temperature.