Twist-controlled imaginary-time Mpemba effect in quantum spin systems

Abstract

We construct a controllable imaginary-time Mpemba effect in quantum spin systems using spatially modulated local rotations without changing initial bipartite entanglement spectra and correlation magnitudes. This feature unambiguously isolates the redistribution of spectral weights as the sole driver of the anomalous relaxation. Using the compact-boson description, we reveal that these twists act as precise mode selectors: higher-harmonic twists exclusively populate high-energy standing waves, structurally bypassing slow-decaying infrared modes to accelerate convergence. We derive exact analytical crossing times for these reversals and demonstrate that intentionally reintroducing the slow-mode population systematically delays the ITME. This exact mechanism is validated beyond the fixed-point theory via calculations on interacting XXZ chains and ladders. Furthermore, a twelve-qubit simulation of variational quantum imaginary-time evolution reproduces the reversals and their controlled delay, providing a concrete route to realize this protocol in realistic quantum circuits. Ultimately, these results provide a strictly controllable and exact starting point for realizing and investigating the imaginary-time Mpemba effect, establishing a foundational paradigm to harness anomalous non-equilibrium relaxation in quantum ground-state preparations.

The paper asks whether imaginary-time Mpemba reversals—an initially higher-energy state reaching a common ground state faster—can be engineered through controlled excitation weights while keeping initial entanglement spectra and correlation magnitudes unchanged. It prepares states by applying sinusoidal products of local $z$ rotations to a known spin-chain ground state. In the compact-boson description, a twist of harmonic $m$ displaces one standing-wave oscillator, with occupation $A_m=K\alpha^2m/2$ and frequency $\omega_m=2\pi vm/L$. Higher harmonics bypass slower modes. Exact Gaussian dynamics gives energy and target-infidelity crossings at $\tau_E=2\tau_I=L\ln(m_h/m_c)/[2\pi v(m_h-m_c)]$. Increasing amplitude at fixed harmonic produces no reversal. Adding the cold harmonic to the hot state with relative amplitude $\gamma$ delays both crossings logarithmically as $\gamma\to1^-$; neither occurs for $\gamma\geq1$. ED, MPS and QMC test the construction in XXZ chains; $L=80$ QMC crossing times agree with compact-boson predictions within about 1%. Additional calculations find reversals in selected Néel-phase chains and finite-width ladders. At the ferromagnetic endpoint, weak-twist theory predicts an $L^2$ energy-crossing scale but no positive-time infidelity crossing. Noiseless twelve-qubit VQITE reproduces crossings with errors below 0.6% at depth six. Exact mode selection and crossing formulas apply at the Gaussian fixed point; lattice momentum selection is weaker and does not guarantee reversals. Some gapped-chain and ladder cases show no resolved reversal. The circuit simulations assume the target ground state is supplied, omit noise, and establish no preparation-resource advantage. Finite-width results do not establish a two-dimensional limit.