TY - JOUR
AB - The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of “precession” and “entanglement” DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.
AU - De Nicola, Stefano
AU - Michailidis, Alexios
AU - Serbyn, Maksym
ID - 9048
IS - 4
JF - Physical Review Letters
KW - General Physics and Astronomy
SN - 0031-9007
TI - Entanglement view of dynamical quantum phase transitions
VL - 126
ER -
TY - JOUR
AB - Relaxation to a thermal state is the inevitable fate of nonequilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional arrays of Rydberg atoms via the mechanism of quantum scars, i.e., initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow us to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with nonconstant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars.
AU - Michailidis, Alexios
AU - Turner, C. J.
AU - Papić, Z.
AU - Abanin, D. A.
AU - Serbyn, Maksym
ID - 8011
IS - 2
JF - Physical Review Research
SN - 2643-1564
TI - Stabilizing two-dimensional quantum scars by deformation and synchronization
VL - 2
ER -
TY - JOUR
AB - The relaxation of few-body quantum systems can strongly depend on the initial state when the system’s semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of “quantum many-body scars,” i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems.
AU - Michailidis, Alexios
AU - Turner, C. J.
AU - Papić, Z.
AU - Abanin, D. A.
AU - Serbyn, Maksym
ID - 7570
IS - 1
JF - Physical Review X
SN - 2160-3308
TI - Slow quantum thermalization and many-body revivals from mixed phase space
VL - 10
ER -
TY - JOUR
AB - Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydbergatom chain, we construct a weak quasilocal deformation of the Rydberg-blockaded Hamiltonian, whichmakes the revivals virtually perfect. Our analysis suggests the existence of an underlying nonintegrableHamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-bodyHilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodicenergy eigenstates—quantum many-body scars. Furthermore, using these insights, we construct a toymodel that hosts exact quantum many-body scars, providing an intuitive explanation of their origin. Ourresults offer specific routes to enhancing coherent many-body revivals and provide a step towardestablishing the stability of quantum many-body scars in the thermodynamic limit.
AU - Choi, Soonwon
AU - Turner, Christopher J.
AU - Pichler, Hannes
AU - Ho, Wen Wei
AU - Michailidis, Alexios
AU - Papić, Zlatko
AU - Serbyn, Maksym
AU - Lukin, Mikhail D.
AU - Abanin, Dmitry A.
ID - 6575
IS - 22
JF - Physical Review Letters
SN - 00319007
TI - Emergent SU(2) dynamics and perfect quantum many-body scars
VL - 122
ER -
TY - JOUR
AB - Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference between the bosonic model realized by superconducting circuits and similar fermionic model is that the effect of the on-site interaction is stronger due to the possibility of multiple excitations occupying the same site. The phase transition is found to be robust upon including longer-range hopping and interaction terms present in the experiments. Furthermore, we calculate experimentally relevant local observables and show that their temporal fluctuations can be used to distinguish between the dynamics of Anderson insulator, many-body localization, and delocalized phases. While we consider unitary dynamics, neglecting the effects of dissipation, decoherence, and measurement back action, the timescales on which the dynamics is unitary are sufficient for observation of characteristic dynamics in the many-body localized phase. Moreover, the experimentally available disorder strength and interactions allow for tuning the many-body localization phase transition, thus making the arrays of superconducting circuit devices a promising platform for exploring localization physics and phase transition.
AU - Orell, Tuure
AU - Michailidis, Alexios
AU - Serbyn, Maksym
AU - Silveri, Matti
ID - 7013
IS - 13
JF - Physical Review B
SN - 2469-9950
TI - Probing the many-body localization phase transition with superconducting circuits
VL - 100
ER -
TY - JOUR
AB - The thermodynamic description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. Recent studies on many-body localization have revealed the existence of systems that strongly violate ergodicity in the presence of quenched disorder. Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems. In the single-particle case, quantum scars correspond to wavefunctions that concentrate in the vicinity of unstable periodic classical trajectories. We show that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space that has recently been experimentally realized in a Rydberg-atom quantum simulator. The quantum scarred eigenstates are embedded throughout the otherwise thermalizing many-body spectrum but lead to direct experimental signatures, as we show for periodic recurrences that reproduce those observed in the experiment. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, opening up opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable.
AU - Turner, Christopher
AU - Michailidis, Alexios
AU - Abanin, Dmitry
AU - Serbyn, Maksym
AU - Papić, Zlatko
ID - 296
JF - Nature Physics
TI - Weak ergodicity breaking from quantum many-body scars
VL - 14
ER -
TY - JOUR
AB - Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien et al., [Nature (London) 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner et al., Nat. Phys. 14, 745 (2018)], such dynamics was attributed to the existence of “quantum scarred” eigenstates in the many-body spectrum of the experimentally realized model. Here, we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify nonergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here, we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit subthermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of “canonical” thermalization.
AU - Turner, C J
AU - Michailidis, Alexios
AU - Abanin, D A
AU - Serbyn, Maksym
AU - Papić, Z
ID - 44
IS - 15
JF - Physical Review B
TI - Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations
VL - 98
ER -
TY - JOUR
AB - Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations.
AU - Michailidis, Alexios
AU - Žnidarič, Marko
AU - Medvedyeva, Mariya
AU - Abanin, Dmitry
AU - Prosen, Tomaž
AU - Papić, Zlatko
ID - 327
IS - 10
JF - Physical Review B
TI - Slow dynamics in translation-invariant quantum lattice models
VL - 97
ER -
TY - JOUR
AB - The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
AU - Maksym Serbyn
AU - Alexios Michailidis
AU - Abanin, Dmitry A
AU - Papić, Zlatko
ID - 984
IS - 16
JF - Physical Review Letters
TI - Power-law entanglement spectrum in many-body localized phases
VL - 117
ER -