Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

Lin, Cheng-Ju; Motrunich, Olexei I.

doi:10.1103/physrevb.96.214301

Cited by 17 publications

(9 citation statements)

References 44 publications

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“…This allowed us to present a complete picture of the nature of coherent transport in the single impurity model. The topic of prethermalisation has been discussed recently [171,321,112], whereby a first stage of relaxation happens to a non-thermal state, followed by true thermalisation as predicted by the ensembles of statistical mechanics at later timescales. Our results suggest that this could be the relaxation mechanism in the single impurity model.…”

Section: Final Remarks and Future Workmentioning

confidence: 99%

Many-Body Localization Dynamics from Gauge Invariance

et al. 2018

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We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow, double-logarithmic entanglement growth are present in a broad regime of parameters-in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ion experiments realizing dynamical gauge fields and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.

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Section: Final Remarks and Future Workmentioning

confidence: 99%

Many-Body Localization Dynamics from Gauge Invariance

et al. 2018

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“…The conjecture above is also supported by the developments in the context of the slowest operators [24,25]. Indeed, for an operator O that commutes with a Hamiltonian H, the time evolution e iHt Oe −iHt is trivial.…”

Section: Introductionmentioning

confidence: 72%

Quasi-conserved quantities in the perturbed XXX spin chain

Malikis,

Kurlov,

Gritsev

2020

Preprint

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We consider the spin-isotropic integrable Heisenberg spin chain weakly perturbed by a local translationally-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we correct them in order to define proper quasi-conserved integrals of motion (charges) for the perturbed model. To achieve this, we exploit the symmetries of the Hamiltonian and introduce a basis for the set of all possible corrections. It is believed that quasi-conserved quantities are responsible for the prethermalization phase at the intermediate timescales. We found that for a sufficiently local perturbation only the first few integrals of motion can be extended to the quasiconserved charges, whereas higher-order integrals of motion die out.

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“…Looking forward, it would be interesting to find new examples of classical and quantum fragmentation that fit into this language, and apply and verify that this formalism applies to the several other examples of Hilbert space fragmentation in the literature [40,41,[44][45][46][47]. An efficient and systematic procedure of determining the commutant corresponding to a family of systems, possibly along the lines of existing works on conserved quantity detection [91][92][93], would be useful in looking for fragmentation, and might also help in finding the associated non-obvious IoMs. These examples can also be used to better understand the finer classification of dynamical phenomena within each of the coarse classes defined by the dimension of the commutant in Tab.…”

Section: Discussionmentioning

confidence: 99%

Hilbert Space Fragmentation and Commutant Algebras

Moudgalya,

Motrunich

2021

Preprint

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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 classical fragmentation, including the t − Jz model and the spin-1 dipole-conserving model, and we illustrate the connection to previously-studied "Statistically Localized Integrals of Motion" (SLIOMs). We also revisit the Temperley-Lieb spin chains, including the spin-1 biquadratic chain widely studied in the literature, and show that they exhibit quantum Hilbert space fragmentation. Finally, we study the contribution of the full commutant algebra to the Mazur bounds in various cases. In fragmented systems, we use expressions for the commutant to analytically obtain new or improved Mazur bounds for autocorrelation functions of local operators that agree with previous numerical results. In addition, we are able to rigorously show the localization of the on-site spin operator in the spin-1 dipole-conserving model.

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Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

Cited by 17 publications

References 44 publications

Many-Body Localization Dynamics from Gauge Invariance

Many-Body Localization Dynamics from Gauge Invariance

Quasi-conserved quantities in the perturbed XXX spin chain

Hilbert Space Fragmentation and Commutant Algebras

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