Quantum

Asymptotic scars arising from the remnants of quantum phase transitions

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Briefings

A new theoretical framework identifies asymptotic quantum many-body scars (AQMBS) as natural remnants of quantum phase transitions in frustration-free Hamiltonians. The study proves that gapless excitations at critical points become AQMBS with energy variance bounded by the excitation gap, with relaxation times governed by dynamic critical exponents. Numerical modeling of the Fredkin and Motzkin chains confirms this, showing exponentially stable AQMBS and volume-law entanglement where the gap closes super-exponentially.

Key points

• AQMBS arise naturally as remnants of quantum phase transitions in frustration-free Hamiltonians, with stability growing as system size increases.
• Gapless excitations at quantum critical points become AQMBS, where energy variance is bounded by the excitation gap and relaxation time scales with dynamic critical exponents.

Context

Quantum many-body scars and ergodicity breaking are established mechanisms in quantum systems. This research provides a theoretical origin for asymptotic quantum many-body scars, linking them to quantum phase transitions in specific Hamiltonian classes.

Limitations

Modeling is limited to Fredkin and Motzkin chains and the two-dimensional PVBS model. Results are based on numerical evidence and theoretical proofs; experimental verification remains pending. Dynamic critical exponents are inferred from gap scaling rather than directly measured.

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