Many-body localization transition in large quantum spin chains: The mobility edge

Chanda, Titas; Sierant, Piotr; Zakrzewski, Jakub

doi:10.1103/physrevresearch.2.032045

Cited by 47 publications

(19 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The strong believe in the existence of MBL phase in the thermodynamic limit (even a proof of it was proposed for a certain class of spin chains [11,12]) was shattered by an influential recent contribution [13], which was followed by a number of works providing arguments for and against the existence of MBL in the thermodynamic limit [14][15][16][17][18][19][20][21]. Similar conclusions could be obtained from approximate time dynamics for large system sizes [22][23][24][25]. In effect, recent claims do suggest the separation of the physical picture into the finite time, finite size, experimentally reachable "MBL regime" leaving the question of the existence of the "MBL phase" in the strict thermodynamic regime open [26][27][28].…”

Section: Introductionmentioning

confidence: 76%

“…Thus, to probe the system, we consider a sample of random initial separable Fock-like states that we choose to lay in the middle of the spectrum. For each realization of the disorder we find states of minimal and maximal energy by density matrix renormalization group (DMRG) algorithm [68,69] and consider random states with energy close to the middle energy (see [24]) for the details about the description of choosing the initial state near a given energy.…”

Section: Model and Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Many-body localization regime for cavity induced long-range interacting models

Chanda,

Zakrzewski

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Many-body localization (MBL) features are studied here for a large spin chain model with long range interactions. The model corresponds to cold atoms placed inside a cavity and driven by an external laser field with long range interactions coming from rescattering of cavity photons. Earlier studies were limited to small sizes amenable to exact diagonalization. It is shown that nonergodic features and MBL may exist in this model for random disorder as well as in the presence of tilted potential on experimental time scales also for experimentally relevant system sizes using tensor networks algorithms.

show abstract

Section: Introductionmentioning

confidence: 76%

Section: Model and Methodsmentioning

confidence: 99%

Many-body localization regime for cavity induced long-range interacting models

Chanda,

Zakrzewski

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus, exact diagonalization with full calculation of all the eigenstates becomes realistic only up to chain lengths 16 L 18 [67]. The spin chains that are frequently used to investigate the MBL phenomenon are known to exhibit strong border effects, meaning that the eigenstates are more localized as they get closer to the boundaries of the band, regardless of the disorder strength [37,39,68,69]. The question of whether true mobility edges survive in the thermodynamic limit in MBL systems is still open as they have also been argued to be indistinguishable from finite size effects [70].…”

Section: Model: the Disordered J 1 -J Chain And Many-body Localizationmentioning

confidence: 99%

Signatures of a critical point in the many-body localization transition

2021

View full text Add to dashboard Cite

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

show abstract

“…In this context, the case of MBL (in one dimension) is special in that it allows for a non-perturbative description in terms of 'l-bits' [33][34][35][36]. Owing to this and to the slow growth of entanglement entropy [37,38], dynamics in the localized phase of MBL systems are by now well explored numerically and analytically [36,[39][40][41][42]; however, these approaches generally fail on the ergodic side of the transition.…”

Section: Introductionmentioning

confidence: 99%

Long-time memory effects in a localizable central spin problem

Rabani²

2022

New J. Phys.

View full text Add to dashboard Cite

We study the properties of the Nakajima-Zwanzig memory kernel for a qubit immersed in a many-body localized (i.e. disordered and interacting) bath. We argue that the memory kernel decays as a power law in both the localized and ergodic regimes, and show how this can be leveraged to extract t → ∞ populations for the qubit from finite time (Jt ≤ 10^2) data in the thermalizing phase. This allows us to quantify how the long-time values of the populations approach the expected thermalized state as the bath approaches the thermodynamic limit. This approach should provide a good complement to state-of-the-art numerical methods, for which the long-time dynamics with large baths are impossible to simulate in this phase. Additionally, our numerics on finite baths reveal the possibility for unbounded exponential growth in the memory kernel, a phenomenon rooted in the appearance of exceptional points in the projected Liouvillian governing the reduced dynamics. In small systems amenable to exact numerics, we find that these pathologies may have some correlation with delocalization.

show abstract

Many-body localization transition in large quantum spin chains: The mobility edge

Cited by 47 publications

References 87 publications

Many-body localization regime for cavity induced long-range interacting models

Many-body localization regime for cavity induced long-range interacting models

Signatures of a critical point in the many-body localization transition

Long-time memory effects in a localizable central spin problem

Contact Info

Product

Resources

About