Renormalization-group study of the many-body localization transition in one dimension

Abstract

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang $\text{et al.}$ [1] and Goremykina $\text{et al.}$ [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length $\zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $\tilde{\zeta }$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $\tilde{\zeta }$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.

arXiv comment9 pages, 4 figures; published in Physical Review B

References in corpus (43)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Unbounded growth of entanglement in models of many-body localization
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Universal slow growth of entanglement in interacting strongly disordered systems
• Many-body localization in a disordered quantum Ising chain
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Stability and instability towards delocalization in MBL systems
• Theory of the many-body localization transition in one dimensional systems
• Extended slow dynamical regime close to the many-body localization transition
• Universal properties of many-body delocalization transitions
• The Ergodic Side of the Many-Body Localization Transition
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• A criterion for many-body localization-delocalization phase transition
• Two universality classes for the many-body localization transition
• Spectral statistics across the many-body localization transition
• Rare region effects and dynamics near the many-body localization transition
• Critical Properties of the Many-Body Localization Transition
• How a small quantum bath can thermalize long localized chains
• Many-body delocalization as a quantum avalanche
• Griffiths effects and slow dynamics in nearly many-body localized systems
• Analytically solvable renormalization group for the many-body localization transition
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Long tail distributions near the many body localization transition
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
• Bimodal entanglement entropy distribution in the many-body localization transition
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
• Multiscale entanglement clusters at the many-body localization phase transition
• Characterizing the many-body localization transition through the entanglement spectrum
• Anomalous thermalization and transport in disordered interacting Floquet systems

Cited by in corpus (75)

• Quantum chaos challenges many-body localization
• Avalanches and many-body resonances in many-body localized systems
• Distinguishing localization from chaos: challenges in finite-size systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Polynomially filtered exact diagonalization approach to many-body localization
• Kinetically constrained freezing transition in a dipole-conserving system
• Many-Body Localization in the Age of Classical Computing
• Many-body localization in a non-Hermitian quasi-periodic system
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• The Many-Body localization transition in the Hilbert space
• Many-body localization near the critical point
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Fock-space correlations and the origins of many-body localisation
• Dynamics and Transport at the Threshold of Many-Body Localization
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Model of level statistics for disordered interacting quantum many-body systems
• Many-body localization from a one-particle perspective in the disordered 1D Bose-Hubbard model
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Localisation on certain graphs with strongly correlated disorder
• Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
• Many-body localization transition in large quantum spin chains: The mobility edge
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
• Local integrals of motion and the quasiperiodic many-body localization transition
• Multifractality and self-averaging at the many-body localization transition
• Many-body localization in large systems: Matrix-product-state approach
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• Detecting delocalization-localization transitions from full density distributions
• The internal clock of many-body delocalization
• Non-thermalized Dynamics of Flat-Band Many-Body Localization
• Extracting many body localization lengths with an imaginary vector potential
• Interaction-Driven Instabilities in the Random-Field XXZ Chain
• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• Mobility edge in long-range interacting many-body localized systems
• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• A note on the quasiperiodic many-body localization transition in dimension $d>1$
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Avalanche stability transition in interacting quasiperiodic systems
• Catching thermal avalanches in the disordered XXZ model
• Many-body localization in long range model: Real space renormalization group study
• Propagation of Many-body Localization in an Anderson Insulator
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• The Fock-space landscape of many-body localisation
• Identifying Correlation Clusters in Many-Body Localized Systems
• Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics
• Breaking the chains: extreme value statistics and localization in random spin chains
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Inverted many-body mobility edge in a central qudit problem
• Quantum criticality in the 2d quasiperiodic Potts model
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Many body localization transition with correlated disorder
• Perturbative instability of non-ergodic phases in non-Abelian quantum chains
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Phenomenology of many-body localization in bond-disordered spin chains
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Hayden-Preskill Recovery in Hamiltonian Systems
• Cat states carrying long-range correlations in the many-body localized phase
• Characterizing the many-body localization transition through correlations
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Interacting quasiperiodic spin chains in the prethermal regime
• Universal properties of single particle excitations across the many-body localization transition
• Spectral Multifractality and Emergent Energyscales Across the Many-Body Localisation Transition
• Anatomy of localisation protected quantum order on Hilbert space
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Many-body localization in a slowly varying potential