Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum

Abstract

Recently, there has been renewed interest in studies of criticality in the spin quantum Hall effect, realized in the Altland-Zirnbauer symmetry class C of disordered, noninteracting fermions in two spatial dimensions. In our study, we develop a nonperturbative analysis of the replica two-dimensional nonlinear sigma model in class C. We explicitly construct the instanton solution with a unit topological charge. By treating fluctuations around the instanton at the Gaussian level, we calculate the instanton correction to the disorder-averaged logarithm of the partition function. We compute non-perturbative corrections to the anomalous dimensions of pure power-law scaling local operators, which determine the spectrum of generalized multifractality. We also calculate instanton corrections to the renormalized longitudinal and Hall spin conductivities and determine the topology of the phase diagram for class C. Our results demonstrate that the spin quantum Hall effect is indeed a close cousin of the integer quantum Hall effect.

21 pages, 3 figures

References in corpus (46)

• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Anderson Transitions
• Periodic table for topological insulators and superconductors
• Statistics of energy levels and eigenfunctions in disordered systems
• Classification of Topological Insulators and Superconductors
• Quasiparticle localization in superconductors with spin-orbit scattering
• Symmetry classes of disordered fermions
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Linking numbers for self-avoiding walks and percolation: application to the spin quantum Hall transition
• Thermal metal in network models of a disordered two-dimensional superconductor
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Towards a Field Theory of the Plateau Transition
• Quantum and classical localisation, the spin quantum Hall effect and generalisations
• Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory
• The integer quantum Hall plateau transition is a current algebra after all
• Magnetic properties of Sr_2Fe_1+xMo_1-xO_6 with -1 <= x <= 0.25
• Surface criticality and multifractality at localization transitions
• Classification and symmetry properties of scaling dimensions at Anderson transitions
• Wave function statistics and multifractality at the spin quantum Hall transition
• Volumes of Compact Manifolds
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• The instanton vacuum of generalized $C{P}^{N-1}$ models
• Boundary criticality and multifractality at the 2D spin quantum Hall transition
• Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime
• Multifractality at the spin quantum Hall transition
• Boundary multifractality in critical 1D systems with long-range hopping
• Gaussian free fields at the integer quantum Hall plateau transition
• Evidence for the PSL(2$|$2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Random network models with variable disorder of geometry
• Disordered d-wave superconductors with interactions
• Scaling collapse of longitudinal conductance near the integer quantum Hall transition
• Metal-insulator transition in a 2D system of chiral unitary class
• Generalized multifractality at spin quantum Hall transition
• Generalized multifractality at metal-insulator transitions and in metallic phases of 2D disordered systems
• Quartic multifractality and finite-size corrections at the spin quantum Hall transition
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Generalized surface multifractality in 2D disordered systems
• Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions
• The integer quantum Hall transition: an $S$-matrix approach to random networks