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arXiv:2308.03622 · Physical review. B./Physical review. B

Phase crossover induced by dynamical many-body localization in periodically driven long-range spin systems

Mahbub Rahaman, Takashi Mori, Analabha Roy

Published Mar 27, 2024• 4 citations
arXivHTMLPDF

Abstract

Dynamical many-body freezing occurs in periodic transverse field-driven integrable quantum spin systems. Under freezing conditions, quantum dynamics causes practically infinite hysteresis in the drive response, maintaining its starting value. We find similar resonant freezing in the Lipkin-Meshkov-Glick (LMG) model. In the LMG, the freezing conditions in the driving field suppresses the heating postulated by the eigenstate thermalization hypothesis (ETH) by inducing dynamical many-body localization, or DMBL. This is in contrast to many-body localization (MBL), which requires disorder to suppress ETH. DMBL has been validated by the inverse participation ratio (IPR) of the quasistationary Floquet modes. Similarly to the TFIM, the LMG exhibits high-frequency localization only at freezing points. IPR localization in the LMG deteriorates with an inverse system size law at lower frequencies, which indicates heating to infinite temperature. Furthermore, adiabatically increasing frequency and amplitude from low values raises the Floquet state IPR in the LMG from nearly zero to unity, indicating a phase crossover. This occurrence enables a future technique to construct an MBL engine in clean systems that can be cycled by adjusting drive parameters only.

DOI
10.1103/physrevb.109.104311

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Dynamical many-body freezing occurs in periodic transverse field-driven integrable quantum spin systems. Under freezing conditions, quantum dynamics causes practically infinite hysteresis in the drive response, maintaining its starting value. We find similar resonant freezing in the Lipkin-Meshkov-Glick (LMG) model. In the LMG, the freezing conditions in the driving field suppresses the heating postulated by the eigenstate thermalization hypothesis (ETH) by inducing dynamical many-body localization, or DMBL. This is in contrast to many-body localization (MBL), which requires disorder to suppress ETH. DMBL has been validated by the inverse participation ratio (IPR) of the quasistationary Floquet modes. Similarly to the TFIM, the LMG exhibits high-frequency localization only at freezing points. IPR localization in the LMG deteriorates with an inverse system size law at lower frequencies, which indicates heating to infinite temperature. Furthermore, adiabatically increasing frequency and amplitude from low values raises the Floquet state IPR in the LMG from nearly zero to unity, indicating a phase crossover. This occurrence enables a future technique to construct an MBL engine in clean systems that can be cycled by adjusting drive parameters only.
Controlling the dynamics of quantum many-body systems is crucial for developing quantum technologies. This work demonstrates that counterdiabatic (CD) driving provides a powerful tool for steering collective spin systems along entangled trajectories for a long time. In particular, CD driving leads to approximate stroboscopic freezing and eternal entanglement oscillations for a large class of initial states in the periodically driven Lipkin-Meshkov-Glick model. Intriguingly, CD driving generates spin squeezing and its associated metrologically useful multipartite entanglement at the mid-point of every drive cycle, when the system is initially prepared in a fully x-polarized state. The CD driving induced nonergodic dynamics is accompanied by a decrease in the average eigenstate entanglement and inverse participation ratio, thereby signaling greater eigenstate localization. Our work opens a new route to evade Floquet heating and control entanglement generation in collective spin systems.
A periodically driven quantum many-body system is believed to approach a locally infinite-temperature-like state as dictated by the ergodicity hypothesis, when all the couplings/parameters are of the same order. When the drive is stronger than a threshold value, a large class of systems is shown to break this mandate, exhibiting Dynamical Freezing (DF): ergodicity is broken due to the emergence of local operators with permanent memory of their initial values (PRX 11, 021008, 2021). However, an exception to DF has recently been noted in a particular setting (PRX 16, 011041, 2026). Here we identify the condition for ergodicity-breaking in a system under strong drive, and show how to stabilize DF by exact, local engineering. We further show that the Floquet Hamiltonian Heff=(i/T)ln⁡[U(T)]H_{eff} = (i/T)\ln{[U(T)]}Heff​=(i/T)ln[U(T)] is non-local when ordered by spin-flips, in a non-DF system, while it turns quasi-local under our simple, local DF engineering that keeps the Hamiltonian H(t)H(t)H(t) still non-integrable at each ttt. This perplexing non-universality is absent in equilibrium, where non-integrability is believed to imply ergodicity and thermalization universally. Our work paves a way to engineering novel ergodicity-broken interacting Floquet phases of matter in various quantum platforms, and also endows DF-assisted quantum error mitigation and state stabilization techniques (see Nature 653, 1027 (2026)) with unprecedented versatility and flexibility.
We show that when a quantum many-body system is subjected to coherent periodic driving, the response may exhibit exotic freezing behavior in high driving frequency $(\ensuremath{\omega})$ regime. In a periodically driven classical thermodynamic system, freezing at high $\ensuremath{\omega}$ occurs when $1/\ensuremath{\omega}$ is much smaller than the characteristic relaxation time of the system and hence the freezing always increases there as $\ensuremath{\omega}$ is increased. Here, in the contrary, we see surprising nonmonotonic freezing behavior of the response with $\ensuremath{\omega}$, showing curious peak-valley structure. Quite interestingly, the entire system tends to freeze almost absolutely (the freezing peaks) when driven with a certain combination of driving parameters values (amplitude and $\ensuremath{\omega}$) due to coherent suppression of dynamics of the quantum many-body modes, which has no classical analog. We demonstrate this new freezing phenomenon analytically (supported by large-scale numerics) for a general class of integrable quantum spin systems.
We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.
Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here we show that, although any randomness in the interactions of a many-body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale $\ensuremath{\tau}$ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down ($\ensuremath{\tau}$ shoots up) by orders of magnitude as the ratio of the drive frequency $\ensuremath{\omega}$ and amplitude h0{h}_{0}h0​ tends to certain specific values (the freezing condition). If $\ensuremath{\omega}$ is increased while maintaining the ratio ${h}_{0}/\ensuremath{\omega}$ at a fixed freezing value, then $\ensuremath{\tau}$ diverges exponentially with $\ensuremath{\omega}.$ The results can be easily extended for a larger family of disordered fermionic and bosonic systems.