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.

19 pages, 16 figures

References in corpus (6)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Phenomenology of fully many-body-localized systems
• Quantum criticality of hot random spin chains
• Strong-disorder renormalization-group study of the one-dimensional tight-binding model

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• 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
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• 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