Strong disorder renormalization group primer and the superfluid-insulator transition

Abstract

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well understood weak disorder theory for this problem allows to illustrate what aspects of the physics change at strong disorder. In particular the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

References in corpus (7)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Phase transition of one dimensional bosons with strong disorder
• Effects of dissipation on a quantum critical point with disorder
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential
• Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires
• Disordered bosons in one dimension: from weak to strong randomness criticality

Cited by in corpus (32)

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• Maximum refractive index of an atomic medium
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• Central charges of aperiodic holographic tensor network models
• Infinite-randomness criticality in monitored quantum dynamics with static disorder
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• Superfluid/Bose-glass transition in one dimension
• Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group
• Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations
• From eigenstate to Hamiltonian: Prospects for ergodicity and localization
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Perturbative instability towards delocalization at phase transitions between MBL phases
• Boundary theories of critical matchgate tensor networks
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• Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass
• Projected Entangled Pair States with flexible geometry
• Strange metal state near quantum superconductor-metal transition in thin films
• Renormalization group analysis of near-field induced dephasing of optical spin waves in an atomic medium
• Subdiffusive spin transport in disordered classical Heisenberg chains
• Kane-Fisher weak link physics in the clean scratched-XY model
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Renormalization-group-inspired neural networks for computing topological invariants
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