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Extreme many-body scarring in a quantum spin chain via weak dynamical constraints

Shane Dooley, Graham Kells

Published Jan 1, 2022• 5 citations
OpenAlex

Abstract

It has recently been established that quantum many-body scarring can prevent the thermalisation of some isolated quantum systems, starting from certain initial states. One of the first models to show this was the so-called PXP Hamiltonian, which was used to theoretically model an experiment on a chain of strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian is a set of dynamical constraints that make certain states inaccessible to the dynamics. In this paper we construct a class of spin chain models that are parameterised by a discrete variable ℓ that controls the "strength" of a dynamical constraint. We show that by increasing ℓ the constraint becomes weaker, in the sense that fewer states are excluded from the dynamics. The PXP Hamiltonian is special case for ℓ=2. By weakening the constraint to ℓ≥4, however, we find a more extreme version of quantum scarring than in the PXP Hamiltonian, with the number of scar states growing exponentially in the system size.

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Extreme many-body scarring in a quantum spin chain via weak dynamical constraints

Shane Dooley, Graham Kells

Thermalization is usually difficult to avoid in large complicated quantum systems. However, it was recently discovered that some models with dynamical constraints can fail to thermalize due to quantum many-body scarring. To explore the connection between dynamical constraints and scarring, the authors here construct a class of spin-chain models in which the strength of the constraints can be tuned. It is observed that the scarring becomes more extreme as the constraint is weakened.

arXiv:2112.06573•Physical review. B./Physical review. B•Apr 15, 2022•7 citations

Quantum many-body scar models in one-dimensional spin chains

Jia-Wei Wang, Xiang-Fa Zhou, Guang‐Can Guo +1 more

The phenomenon of quantum many-body scars has received widespread attention both in theoretical and experimental physics in recent years due to its unique physical properties. In this paper, based on the su(2) algebraic relations, we propose a general method for constructing scar models by combining simple modules. This allows us to investigate many-body scar phenomena in high-spin systems. We numerically verify the thermalization and nonintegrability of this model and demonstrate the dynamical properties of the scar states. We also provide a theoretical analysis of the properties of these scar states. For spin-1 case, we find that our 1D chain model reduces to the famous PXP model [C. J. Turner et al., Phys. Rev. B 98, 155134 (2018)] under special parameter conditions. In addition, due to the continuous tunability of the parameters, our model also enables us to investigate the transitions of quantum many-body scar phenomena from nonintegrable to integrable system.

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Hypergrid subgraphs and the origin of scarred quantum walks in many-body Hilbert space

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Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in nonintegrable quantum systems. Here we explore the origin of scarred wave function revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model---the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.

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Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.

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Pronounced quantum many-body scars in the one-dimensional spin-1 Kitaev model

Sashikanta Mohapatra, Ajit Coimbatore Balram

Experimental observation of coherent oscillations in a Rydberg atom chain [H. Bernien et al., Nature (London) 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBSs) which is a new paradigm for ergodicity breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the ``PXP'' model, which has been shown to host the eigenstate thermalization hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this paper, we study the QMBSs that can arise in one such model, namely the spin-1 Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Res. 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are pronounced and longer lived than those in the PXP model.

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Bridging quantum criticality via many-body scarring

Aiden Daniel, Andrew Hallam, Jean-Yves Desaules +4 more

Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.

arXiv:2301.03631•Physical review. B./Physical review. B•Jun 5, 2023•20 citations
It has recently been established that quantum many-body scarring can prevent the thermalisation of some isolated quantum systems, starting from certain initial states. One of the first models to show this was the so-called PXP Hamiltonian, which was used to theoretically model an experiment on a chain of strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian is a set of dynamical constraints that make certain states inaccessible to the dynamics. In this paper we construct a class of spin chain models that are parameterised by a discrete variable ℓ that controls the "strength" of a dynamical constraint. We show that by increasing ℓ the constraint becomes weaker, in the sense that fewer states are excluded from the dynamics. The PXP Hamiltonian is special case for ℓ=2. By weakening the constraint to ℓ≥4, however, we find a more extreme version of quantum scarring than in the PXP Hamiltonian, with the number of scar states growing exponentially in the system size.
The phenomenon of quantum many-body scars has received widespread attention both in theoretical and experimental physics in recent years due to its unique physical properties. In this paper, based on the su(2) algebraic relations, we propose a general method for constructing scar models by combining simple modules. This allows us to investigate many-body scar phenomena in high-spin systems. We numerically verify the thermalization and nonintegrability of this model and demonstrate the dynamical properties of the scar states. We also provide a theoretical analysis of the properties of these scar states. For spin-1 case, we find that our 1D chain model reduces to the famous PXP model [C. J. Turner et al., Phys. Rev. B 98, 155134 (2018)] under special parameter conditions. In addition, due to the continuous tunability of the parameters, our model also enables us to investigate the transitions of quantum many-body scar phenomena from nonintegrable to integrable system.
Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in nonintegrable quantum systems. Here we explore the origin of scarred wave function revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model---the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.
Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.
Experimental observation of coherent oscillations in a Rydberg atom chain [H. Bernien et al., Nature (London) 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBSs) which is a new paradigm for ergodicity breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the ``PXP'' model, which has been shown to host the eigenstate thermalization hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this paper, we study the QMBSs that can arise in one such model, namely the spin-1 Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Res. 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are pronounced and longer lived than those in the PXP model.
Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.