Localization transition in one dimension using Wegner flow equations

Abstract

The flow equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent $\alpha$. We derive the flow equations, and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for $\alpha <1/2$. Additionally, in the regime, $\alpha >1/2$, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point $\left(\alpha =1\right)$. This method correctly reproduces the critical level-spacing statistics, and the fractal dimensionality of the eigenfunctions.

arXiv comment19 pages, 16 figures

References in corpus (30)

• Random-Matrix Theory of Quantum Transport
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• 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
• 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
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Theory of the many-body localization transition in one dimensional systems
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• A random matrix model with localization and ergodic transitions
• Spectral statistics across the many-body localization transition
• Explicit Local Integrals of Motion for the Many-Body Localized State
• Integrability of a disordered Heisenberg spin-1/2 chain
• Quantum criticality of hot random spin chains
• Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time
• Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
• Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
• Symmetries of multifractal spectra and field theories of Anderson localization
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• $1/f^{\alpha }$ noise and generalized diffusion in random Heisenberg spin systems
• Strong-disorder renormalization-group study of the one-dimensional tight-binding model
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion

Cited by in corpus (21)

• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Fixed points of Wegner-Wilson flows and many-body localization
• Strong Disorder RG approach - a short review of recent developments
• Self-dual quasiperiodic systems with power-law hopping
• Critical properties of the Anderson localization transition and the high dimensional limit
• Dynamics and Transport at the Threshold of Many-Body Localization
• A microscopic description of acid-base equilibrium
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Localization-enhanced and degraded topological-order in interacting p-wave wires
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations
• Genuine localisation transition in a long-range hopping model
• Dissipative flow equations
• Flow Equations for Disordered Floquet Systems
• Fate of Algebraic Many-Body Localization under driving
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians