Exact projector Hamiltonian, local integrals of motion, and many-body localization with symmetry-protected topological order

Orito, Takahiro; Kuno, Yoshihito; Ichinose, Ikuo

doi:10.1103/physrevb.101.224308

Cited by 23 publications

(17 citation statements)

References 41 publications

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“…This phenomenon, coined many-body flatband localization, implies strict localization of particles (interaction or single-particle Hamiltonian is semidetangled) and in addition heat (both are fully detangled) irrespective of dimensionality or interaction strength, and it does not require vastly different energy scales similar to some models supposed to exhibit disorder-free MBL. Our work substantially extends previous studies of localization phenomena of interacting quantum many-body platforms with all-band-flat lattice single-particle Hamiltonians [44,46,[58][59][60][61][62][63][64]. In particular, we propose a flexible and general set of many-body localized systems which may be experimentally feasible.…”

supporting

confidence: 62%

Many-body flatband localization

2020

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We generate translationally invariant systems exhibiting many-body localization from all-bands-flat singleparticle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon, dubbed many-body flatband localization, is based on symmetries of both single-particle and interaction terms in the Hamiltonian, and it holds for any interaction strength. We propose a generator of corresponding Hamiltonians which covers both interacting bosons and fermions for arbitrary lattice dimensions, and we provide explicit examples of such models in one and two lattice dimensions. We also explicitly construct an extensive set of local integrals of motion for this set of models. Our results can be further generalized to long-range interactions as well as to systems lacking translational invariance.

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confidence: 62%

Many-body flatband localization

2020

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“…Recently many-particles CLS [35][36][37] and flatband-induced quantum scars [38][39][40] have been introduced. Networks which completely lack single particle dispersion (all bands flat), can completely suppress charge transport with fine-tuned interaction [41][42][43], while adding onsite disorder and interactions leads to conventional MBL features [44]. We show that disorder free MBL needs just one flatband and at least one dispersive band when accompanied with a proper interaction finetuning.…”

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confidence: 90%

Many-body localization transition from flatband fine-tuning

Danieli,

Andreanov,

Flach

2021

Preprint

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Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two-body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.

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“…As a consequence, exotic phases of matter with unusual properties emerge under the effect of various perturbations: disorder, [32][33][34][35][36] external fields, [37][38][39] nonlinearities. [40][41][42] Interactions in FB lead to a plethora of interesting phenomena: delocalisation and conserved quantities, [43][44][45][46] disorder free many-body localisation, 45,[47][48][49] groundstate ferromagnetism, 8,9,13,[50][51][52][53] pair formation for hard core bosons, 54 superfluidity, [55][56][57] and superconductivity. 58 However the very defining feature of the flatbandstheir fine-tuned degeneracy -makes it difficult to identify them in the relevant Hamiltonian parameter space.…”

Section: Introductionmentioning

confidence: 99%

Flatband generator in two dimensions

Maimaiti,

Andreanov,

Flach

2021

Preprint

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Dispersionless bands -flatbands -provide an excellent testbed for novel physical phases due to the fine-tuned character of flatband tight-binding Hamiltonians. The accompanying macroscopic degeneracy makes any perturbation relevant, no matter how small. For short-range hoppings flatbands support compact localized states, which allowed to develop systematic flatband generators in d = 1 dimension in Phys. Rev. B 95 115135 (2017) and Phys. Rev. B 99 125129 (2019). Here we extend this generator approach to d = 2 dimensions. The shape of a compact localized state turns into an important additional flatband classifier. This allows us to obtain analytical solutions for classes of d = 2 flatband networks and to re-classify and re-obtain known ones, such as the checkerboard, kagome, Lieb and Tasaki lattices. Our generator can be straightforwardly generalized to three lattice dimensions as well.

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Exact projector Hamiltonian, local integrals of motion, and many-body localization with symmetry-protected topological order

Cited by 23 publications

References 41 publications

Many-body flatband localization

Many-body flatband localization

Many-body localization transition from flatband fine-tuning

Flatband generator in two dimensions

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