Quantum many-body scars in spin-1 Kitaev chains

You, Wen-Long; Zhao, Zhuan; Ren, Jiliang; Sun, Gaoyong; Li, Liangsheng; Oleś, Andrzej M.

doi:10.1103/physrevresearch.4.013103

Cited by 20 publications

(14 citation statements)

References 74 publications

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“…Specifically, this work opens up possibilities to extend for other Z symmetric state (e.g., like |Z 3 , |Z 4 ) with and without perturbation. Another interesting future direction will be to study the behavior of complexity beyond the PXP model such as higher spin [102,103], periodically driven systems [104][105][106][107], and hypercube models [108].…”

Section: Discussionmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Néel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such "closeness" by the q-deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Néel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Néel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.

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Section: Discussionmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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“…The S > 1 2 Kitaev chain was considered in Ref. [39] and the S=1 model in zero field has been the subject of several studies [40][41][42][43], however, to our knowledge the phase diagram in the presence of a magnetic field has not previously been investigated, likely since it has been assumed that the model would transition to the polarized phase without any intervening non-trivial phases as has been shown to be the case for the S= 1 2 chain in a transverse magnetic field [44]. However, it turns out that if more general field directions are considered a highly nontrivial soliton phase can be identified in the S= 1 2 chain [37], appearing along the field directions φ xy = π 4 +n π 2 .…”

Section: Model Phase Diagram and Phenomenologymentioning

confidence: 99%

Islands of Chiral Solitons in Integer Spin Kitaev Chains

Sørensen¹,

Riddell²

2023

Preprint

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An intriguing chiral soliton phase has recently been identified in the S= 1 2 Kitaev spin chain. Here we show that for S=1,2,3,4,5 an analogous phase can be identified, but contrary to the S= 1 2 case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiabatically connect the integer spin Kitaev chain to the polarized phase. Only at sizable intermediate fields along symmetry directions does the soliton phase appear centered around the special point h x =h y =S where two exact product ground-states can be identified. The large S limit can be understood from a semi-classical analysis, and variational calculations provide a detailed picture of the S=1 soliton phase. Under open boundary conditions, the chain has a single soliton in the ground-state which can be excited, leading to a proliferation of in-gap states. In contrast, even length periodic chains exhibit a gap above a twice degenerate ground-state. The presence of solitons leaves a distinct imprint on the low temperature specific heat.

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“…discrete, driven versions of time crystals under dissipation [64][65][66][67][68][69][70] and other non-stationary phenomena beyond ob-servables e.g. [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]). As the oscillations in our model are persistent in the thermodynamic limit, the model may be understood as a boundary time pseudo-crystal, with pseudo-implying that the oscillations amplitude decays with the system size for initial states with low entanglement, similarly to long-range order in a pseudocondensate [87].…”

Section: Introductionmentioning

confidence: 99%

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Alaeian¹,

Buča²

2022

Preprint

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The existence of bistability in quantum optical systems remains a intensely debated open question beyond the mean-field approximation. Quantum fluctuations are finite-size corrections to the mean-field approximation used because the full exact solution is unobtainable. Usually, quantum fluctuations destroy the bistability present on the mean-field level. Here, by identifying and using exact modulated semi-local dynamical symmetries in a certain quantum optical models of drivendissipative fermionic chains we exactly prove bistability in precisely the quantum fluctuations. Surprisingly, rather than destroying bistability, the quantum fluctuations themselves exhibit bistability, even though it is absent on the mean-field level for our systems. Moreover, the models studied acquire additional thermodynamic dynamical symmetries that imply persistent periodic oscillations in the quantum fluctuations, constituting pseudo-variants of boundary time crystals. Physically, these emergent operators correspond to finite-frequency and finite-momentum semi-local Goldstone modes. Our work therefore provides to the best of our knowledge the first example of a provably bistable quantum optical system.

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Quantum many-body scars in spin-1 Kitaev chains

Cited by 20 publications

References 74 publications

Probing quantum scars and weak ergodicity breaking through quantum complexity

Probing quantum scars and weak ergodicity breaking through quantum complexity

Islands of Chiral Solitons in Integer Spin Kitaev Chains

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

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