Initial State Dependent Dynamics Across Many-body Localization Transition

Abstract

We investigate quench dynamics across many-body localization (MBL) transition in an interacting one dimensional system of spinless fermions with aperiodic potential. We consider a large number of initial states characterized by the number of kinks, $N_{kinks}$, in the density profile. On the delocalized side of the MBL transition the dynamics becomes faster with increase in $N_{kinks}$ such that the decay exponent, $\gamma$, in the density imbalance increases with increase in $N_{kinks}$. The growth exponent of the mean square displacement which shows a power-law behaviour $⟨x^2(t)⟩\sim t^{\beta }$ in the long time limit is much larger than the exponent $\gamma$ for 1-kink and other low kink states though $\beta \sim 2\gamma$ for a charge density wave state. As the disorder strength increases ${\gamma }_{N_{kink}}\to 0$ at some critical disorder, $h_{N_{kinks}}$ which is a monotonically increasing function of $N_{kinks}$. A 1-kink state always underestimates the value of disorder at which the MBL transition takes place but $h_{1-kink}$ coincides with the onset of the sub-diffusive phase preceding the MBL phase. This is consistent with the dynamics of interface broadening for the 1-kink state. We show that the bipartite entanglement entropy has a logarithmic growth $a\ln (Vt)$ not only in the MBL phase but also in the delocalised phase and in both the phases the coefficient $a$ increases with $N_{kinks}$ as well as with the interaction strength $V$. We explain this dependence of dynamics on the number of kinks in terms of the normalized participation ratio of initial states in the eigenbasis of the interacting Hamiltonian.

14 pages, 12 figures

References in corpus (14)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• The Kernel Polynomial Method
• Many-body localization edge in the random-field Heisenberg chain
• Many-Body Localization in a Quasiperiodic System
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Recent progress in many-body localization
• Typicality for Generalized Microcanonical Ensembles
• Challenges to observation of many-body localization
• Chebyshev matrix product state approach for spectral functions
• Extended nonergodic states in disordered many-body quantum systems
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?

Cited by in corpus (6)

• Many-Body Localization in the Age of Classical Computing
• Exploring Hilbert-Space Fragmentation on a Superconducting Processor
• Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Universal properties of single particle excitations across the many-body localization transition
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization