Tunable many-body burst in isolated quantum systems

TL;DR

This work shows that a burst—an atypical transient deviation of a local observable from its equilibrium value—can be engineered from a low-entangled initial state in a nonintegrable quantum chain. By combining two MPS-based methods (time-reversed truncation and DMRG-optimized cost functions), the authors tailor initial states to produce bursts at a designated time $\tau$, while observing slow or negative entanglement growth beforehand. A local random-circuit analysis provides probabilistic bounds, revealing that such bursts become exponentially rare at long times, implying that nonequilibrium states can persist briefly before scrambling dominates. The findings offer a framework for experimentally testing nonmonotonic thermalization, with implications for quantum metrology and the study of ETH-related dynamics in programmable quantum simulators.

Abstract

Thermalization in isolated quantum many-body systems can be nonmonotonic, with its process dependent on an initial state. We propose a numerical method to construct a low-entangled initial state that creates a ``burst''$\unicode{x2013}\unicode{x2013}$a transient deviation of an observable from its thermal equilibrium value$\unicode{x2013}\unicode{x2013}$at a designated time. We apply this method to demonstrate that a burst of magnetization can be realized for a nonintegrable mixed-field Ising chain on a timescale comparable to the onset of quantum scrambling. Contrary to the typical spreading of information in this regime, the created burst is accompanied by a slow or even negative entanglement growth. Analytically, we show that a burst becomes probabilistically rare after a long time. Our results suggest that a nonequilibrium state is maintained for an appropriately chosen initial state until scrambling becomes dominant. These predictions can be tested with programmable quantum simulators.

Figures (5)

• Figure 1: Time evolution of the expectation value $\langle O(t)\rangle$ (solid) and that of entanglement entropy $S_\mathcal{A}(t)$ (dash-dotted, calculated for the half system $\mathcal{A}=\{1,2,\ldots,\lfloor L/2 \rfloor\}$) with $L=40$ for the mixed-field Ising chain \ref{['eq:Ising']}. A dashed line indicates the thermal equilibrium value of $O$. Initial states are obtained by Method 2 with $\tau=20$, $\chi=10$, $\beta=0.1$, and $\lambda_L=72/L^2$. (a) Case of $O=M^y$. (b) Case of $O=M^z$. Note that $\langle M^z\rangle_\mathrm{eq}$ is slightly below zero.
• Figure 2: Burst amplitude $\langle O\rangle_\mathrm{eq}-\langle O(\tau) \rangle$ versus the burst time $\tau$ with respect to different system sizes $L$ for the mixed-field Ising chain \ref{['eq:Ising']}. Initial states are obtained by Method 2 with $\chi=10$, $\beta=0.1$, and $\lambda_L=72/L^2$. (a) Case of $O=M^y$. (b) Case of $O=M^z$.
• Figure 3: Schematic illustration of a quantum circuit that creates an approximate MPS $\ket{\psi_\mathrm{app}}$ with $L=5$ spins and $K=2$ layers.
• Figure 4: Comparison of the time evolution between the target MPS $\ket{\psi_0}$ (gray) and its quantum circuit (QC) approximation $\ket{\psi_\mathrm{app}}$ (blue) with $L=40$ for the mixed-field Ising chain \ref{['eq:Ising']}. A solid curve and a dash-dotted curve represent the time evolution of the expectation value $\langle O(t)\rangle$ and that of entanglement entropy $S_\mathcal{A}(t)$ calculated for the half system $\mathcal{A}=\{1,2,\ldots,\lfloor L/2 \rfloor\}$, respectively. For gray curves, initial states are obtained by Method 2 with $\tau=20$, $\chi=10$, $\beta=0.1$, and $\lambda_L=72/L^2$. For blue curves, initial states are prepared by staircase quantum circuits of $K=5$ layers that approximate the exact MPSs. (a) Case of $O=M^y$. (b) Case of $O=M^z$.
• Figure 5: Burst amplitude $\langle O\rangle_\mathrm{eq}-\langle O(\tau) \rangle$ versus the burst time $\tau$ in the thermodynamic limit for the mixed-field Ising chain \ref{['eq:Ising']}. Initial states are obtained by Method 1 with $\chi=10$, and a gray curve shows the average truncation error of the two bonds in an iMPS. (a) Case of $O=M^y$. (b) Case of $O=M^z$.

Theorems & Definitions (13)

• Definition 1: Definition 1 of Brandao2016-design
• Lemma 2: Theorem 5 of Brandao2016-design
• Lemma 3
• proof
• Definition 4: Definition 2.2 of Low2009-design
• Definition 5: Definition 2.6 of Low2009-design
• Lemma 6: Lemma 2.2.14 of Low2010-design
• Lemma 7: Theorem 1.2 of Low2009-design
• Proposition 8: Eq. \ref{['eq:LRProb']} in the main text
• proof