Localization of interacting fermions at high temperature

Oganesyan, Vadim; Huse, David A.

doi:10.1103/physrevb.75.155111

Cited by 1,699 publications

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“…Such special cases, corresponding to integrable (and thus non-chaotic) dynamics, were thought to be fine-tuned points rather than stable dynamical phases. However, in recent years, a stable, nonthermalizing specifically quantum phase known as the 'many-body-localized' (MBL) phase, has been predicted to exist in certain systems [7][8][9][10][11]. The MBL phase is not known to have any direct classical equivalent [12,13], and unlike traditional integrable systems is, moreover, robust against generic local perturbations to the system's Hamiltonian, so is not fine-tuned.…”

Section: Introductionmentioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

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Section: Introductionmentioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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“…Since such a transition in fact implies a qualitative change of character of MB states across the eigenspectrum it as relevant and highly nontrivial to study systems at high T → ∞. [11] In this context, recent studies of energy-level statistics, [11] the effective hopping in the configuration space [12] and the decay of correlation functions [13] indicate a possible MB localization at very large disorder strength W . [12] The conclusions from the scaling analysis of the conductivity of such models appear similar, [14] as well as the time evolution and the entanglement of wave-functions is concerned.…”

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confidence: 99%

“…We adopt the view that possible conductor-insulator transition needs to be a manifestation of the character of MB quantum states [11,12,15] (hence not directly related to other thermodynamic quantities). Therefore one may as well restrict the study to the regime T → ∞, β → 0, where all MB states contribute with equal weight to σ(ω).…”

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confidence: 99%

Conductivity in a disordered one-dimensional system of interacting fermions

Barišić

Prelovšek

2010

Phys. Rev. B

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Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing d.c. transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the d.c. conductivity σ0 scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase of the effective localization length with the interaction. So far, firm results and conclusions have been reached for the T = 0 ground state of 1D tight-binding fermionic system with a diagonal Anderson disorder. In particular, it has been shown by the density-matrix renormalization-group (DMRG) numerical studies [5,6] that in spite of correlations the manybody (MB) states remain localized, preventing the d.c. transport. The T > 0 behavior appears to be much harder to deal with [7,8] and, at present, the existence of MB localization beyond the ground state is controversial.[9] The most interesting conjecture emerging from an involved analytical calculation[10] predicts a finite-temperature phase transition between the MB insulator at T < T * and a conductor at T > T * . Since such a transition in fact implies a qualitative change of character of MB states across the eigenspectrum it as relevant and highly nontrivial to study systems at high T → ∞. On the other hand, recent direct numerical evaluation of the T > 0 transport coefficients in disordered anisotropic XXZ model [16] (model being equivalent in 1D to a tight-binding fermionic system with nearest-neighbor interaction) does not show any indication of a crossover to a MB localization at low T or at larger W . This questions the conductor-insulator phase diagram and the relation to above mentioned studies.Our aim is to extend previous numerical study [16] of transport properties of the 1D disordered system, modeled by the t-V model of spinless fermions, in order to explore the phase diagram at high T with respect to the d.c. conductivity σ 0 . In contrast to most previous works, in which the interaction strength ∆ = V /(2t) has been mainly kept fixed and possible MB localization has been considered at large disorder values W , we start with a disordered system of NI electrons (∆ = 0), characterized by the vanishing d.c. transport at all T , i.e. σ 0 = 0. By increasing gradually, at fixed W , the repulsive interaction ∆ > 0 we monitor a possible conductor-insulator transition in σ 0 . Dealing with a finite-size system, instead of a singular behavior we expect that the insulator-transition transition should manifest itself as a crossover in σ 0 vs. ∆. This crossover can be then used as a signature of a qualitative (gradual or abrupt) change of MB states with respect to the d.c. transport in the thermodynamic limit T → ∞. As the prototype mod...

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“…One prominent result is the (LiebRobinson) linear in-time growth of entanglement in ballistic and diffusive systems 12 . By contrast, there exist localized interacting many-body systems, known as "manybody localized" phases [13][14][15][16][17][18][19][20][21][22] , whose subsystems' entanglement grows only logarithmically in time 16,[23][24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

“…to finite statistical entropy density vis-a-vis finite excitation energy density) these behaviors are encoded in the entanglement of many-body eigenstates -exhibiting surface law in localized phases and volume law otherwise. Latter behavior is usually related to "eigenstate thermalization hypothesis" 15,[27][28][29][30] . On the contrary, MBL phases display a -possibly partially-localized spectrum and a correspondent mobility edge [31][32][33][34][35] .…”

Section: Introductionmentioning

confidence: 99%

Multipoint entanglement in disordered systems

2017

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We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases -MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states within the localized phase -some of these show considerable generation and delocalization of quantum information.

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Localization of interacting fermions at high temperature

Cited by 1,699 publications

References 17 publications

Rare‐region effects and dynamics near the many‐body localization transition

Rare‐region effects and dynamics near the many‐body localization transition

Conductivity in a disordered one-dimensional system of interacting fermions

Multipoint entanglement in disordered systems

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