Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z50: Quantum Many-Body ScarsRecordings Available
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Sponsoring Units: DCMP Chair: Sanjay Moudgalya, Caltech Room: McCormick Place W-474A |
Friday, March 18, 2022 11:30AM - 11:42AM |
Z50.00001: Hilbert Space Fragmentation and Commutant Algebras Sanjay Moudgalya, Olexei I Motrunich We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of the circuit. We provide a precise definition of Hilbert space fragmentation in this formalism as the case where the dimension of the commutant algebra grows exponentially with the system size. Fragmentation can hence be distinguished from systems with conventional symmetries such as U(1) or SU(2), where the dimension of the commutant algebra grows polynomially with the system size. Further, the commutant algebra language also helps distinguish between "classical" and "quantum" Hilbert space fragmentation, where the former refers to fragmentation in the product state basis. We explicitly construct the commutant algebra in several systems exhibiting fragmentation, discuss the connection to previously-studied "Statistically Localized Integrals of Motion" (SLIOMs), and analytically obtain new or improved Mazur bounds for autocorrelation functions of local operators that explain previous numerical results. In addition, we show how Quantum Many-Body Scars, a related form of weak ergodicity breaking, can be captured within a similar framework of commutant algebras. |
Friday, March 18, 2022 11:42AM - 11:54AM |
Z50.00002: Subdiffusion and many-body quantum chaos with kinetic constraints Hansveer Singh, Brayden A Ware, Aaron J Friedman, Romain Vasseur We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian−or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, tTh, determined by the spectral form factor, to transport properties and linear response correlators. Using tensor network methods, we determine the dynamical exponent, z, for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with 'Fredkin constraints' exhibit anomalous transport with dynamical exponent z?8/3. |
Friday, March 18, 2022 11:54AM - 12:06PM |
Z50.00003: Quantum many-body scars in Floquet magnetic systems Ronald Melendrez, Arijeet Pal, Hitesh J Changlani Recent experimental and theoretical works have found athermal behavior for quench dynamics of specially prepared initial states in an otherwise nonintegrable clean system in one dimension. These have been dubbed as quantum many-body scars (QMBS). Building on our previous work [K.Lee et al., Phys. Rev. B 101, 241111(R) (2020)] which demonstrated the presence of QMBS with perfect revivals in high dimensional magnetic systems in a magnetic field, we explore the question of their stability under Floquet driving. We study the periodically driven bond-alternating spin-1/2 nearest neighbor XXZ Hamiltonian and its two-dimensional equivalent on the highly frustrated kagome lattice. These models harbor a manifold of zero modes which remain stable to certain driving protocols. We characterise the non-equilibrium dynamics and the enhanced coherence of a class of initial states. Our models and the corresponding findings for these nonequilibrium relaxation effects are potentially realizable on current ion trap setups, and we also discuss the feasibility of observing them in real materials. |
Friday, March 18, 2022 12:06PM - 12:18PM |
Z50.00004: Interplay between kinematic constraint and random disorder in 2D PXP model Ke Huang, Yu Wang, Xiao Li Kinematic constraint is known to generate quantum many-body scars in the PXP model, which explaining the weak ergodicity breaking in Rydberg-atom experiments. Meanwhile, random disorders can bring a closed quantum system into the many-body localization phase. In a recent work (arXiv: 2102.08241) we studied the 2D PXP model in the presence of different types of random disorders. We show that the scar states can be stable up to a finite disorder strength before eventually been destroyed. Further, the dynamics of the Neel state also indicates the weak ergodicity breaking in this case. In the presence of strong disorders, however, we find that disorders compatible with the kinematic constraint are still able to localize the system. In contrast, other types of disorders are prohibited by the kinematic constraint to localize the system. |
Friday, March 18, 2022 12:18PM - 12:30PM |
Z50.00005: Dynamics in Systems with Modulated Symmetries Pablo Sala de Torres-Solanot, Julius Lehmann, Tibor Rakovszky, Frank Pollmann We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two and three dimensions. Seeking to understand their effect in the long-time dynamics, we numerically study a stochastic cellular automaton evolution that obeys such symmetries. We prove that in one dimension, the periodically modulated symmetries lead to a diffusive scaling of correlations modulated by a finite microscopic momentum. In higher dimensions, these symmetries take the form of lines and surfaces of conserved momenta. These give rise to exotic forms of sub-diffusive behavior with a rich spatial structure influenced by lattice-scale features. Exponential modulation, on the other hand, can lead to correlations that are infinitely long-lived at the boundary, while decaying exponentially in the bulk. |
Friday, March 18, 2022 12:30PM - 12:42PM |
Z50.00006: Quantum local random networks and the statistical robustness of quantum scars Federica Maria Surace, Alessandro Silva, Marcello Dalmonte We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call ``statistical", and we identify specific signatures of the localized nature of these eigenstates by analyzing a combination of indicators of quantum ergodicity and properties related to the network structure of the model. Within this parallelism, we associate the emergence of statistical scars to the presence of ``motifs" in the network, that reflects how these are associated to links with anomalously small connectivity. Most remarkably, statistical scars appear at well-defined values of energy, predicted solely on the base of network theory. We study the scaling of the number of statistical scars with system size: by continuously changing the connectivity of the system we find that there is a transition from a regime where the constraints are too weak for scars to exist for large systems to a regime where constraints are stronger and the number of statistical scars increases with system size. This allows to the define the concept of ``statistical robustness" of quantum scars. |
Friday, March 18, 2022 12:42PM - 12:54PM |
Z50.00007: Scars and Fragmented Hamiltonians from Automaton circuits Pierre-Gabriel Rozon, Michael J Gullans, Kartiek Agarwal Classical cellular automata can be recast as Floquet unitary circuits, and have been recently studied for hosting a variety of interesting dynamical properties. These circuits naturally exhibit Hilbert space fragmentation, with subspaces comprising of orbits of computational basis states that are cycled through with successive applications of the unitary circuit. It is natural to ask if Hamiltonians exhibiting a similar fragmented structure can be derived from such automaton circuits. In this work, we investigate this question in detail and show how certain restrictions on the local unitaries composing these circuits allow for a convergent BCH expansion which further allows us to define effective local Hamiltonians that exhibit exact and approximate scars, as well as weak and strong fragmentation. |
Friday, March 18, 2022 12:54PM - 1:06PM |
Z50.00008: Generalized η-pairing States in Extended SU(N) Hubbard Models Hironobu Yoshida, Hosho Katsura η-pairing states are exact eigenstates of the SU(2) Hubbard model that exhibit two-particle off-diagonal long-range order (ODLRO) [1]. Although these states are not ground states, there has been a recent surge of interest in such states in the context of superconductivity and superfluidity, and quantum many-body scars. Recently, the SU(N) generalization of the Hubbard model has attracted much attention since it was realized with ultracold atoms in optical lattices [2]. Despite its obvious importance, the counterpart of η-pairing states in the SU(N) (N > 2) Hubbard model was missing. |
Friday, March 18, 2022 1:06PM - 1:18PM |
Z50.00009: Quantum many-body scars in tilted optical lattices Ana Hudomal, Jean-Yves M Desaules, Christopher J Turner, Zlatko Papic Ultracold atoms in optical lattices provide a versatile and finely tunable platform for the study of non-equilibrium many-body phenomena. Quantum many-body scars -- a form of weak ergodicity breaking -- have been found in a variety of theoretical models, but their experimental realizations remain scarce. We numerically investigate a tilted 1D optical lattice and find characteristic signatures of quantum many-body scarring, including persistent dynamical revivals, slow growth of entanglement entropy, and the presence of non-thermalizing eigenstates. These signatures of weak ergodicity breaking occur near commensurable values of tilt and interaction energy scales, and their origin is shown to be related to the emergence of regular substructures in the adjacency graph of the model. |
Friday, March 18, 2022 1:18PM - 1:30PM |
Z50.00010: Quantum many-body scars have extensive multipartite entanglement Jean-Yves M Desaules, Francesca Pietracaprina, Zlatko Papic, John Goold, Silvia Pappalardi Recent experimental observation of weak ergodicity breaking in Rydberg atom quantum simulators has sparked interest in quantum many-body scars - eigenstates which evade thermalisation at finite energy densities due to novel mechanisms that do not rely on integrability or protection by a global symmetry. A salient feature of quantum many-body scars is their sub-volume bipartite entanglement entropy. In this work we demonstrate that exact many-body scars also possess extensive multipartite entanglement structure. We show this analytically, through a scaling of the quantum Fisher information density, which is found to be extensive for scarred eigenstates in contrast to generic thermal states. Furthermore, we numerically study signatures of multipartite entanglement in the PXP model of Rydberg atoms, showing that extensive quantum Fisher information can be generated dynamically by performing a global quench experiment. Our results identify a rich multipartite correlation structure of scarred states with significant potential as a resource in quantum enhanced metrology. |
Friday, March 18, 2022 1:30PM - 1:42PM |
Z50.00011: Construction of quantum many-body scars in higher-dimensional spinless fermion systems Kensuke Tamura, Hosho Katsura The recent experiment on Rydberg atoms [1] observed anomalously slow thermalizing dynamics from certain initial states, even though the system is non-integrable. This behavior originates from the existence of quantum many-body scarred (QMBS) states, which are non-thermal states violating the eigenstate thermalization hypothesis. |
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