Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

Abstract

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon )\propto (1/x{)}^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_{\epsilon }\propto {\ln }^2(1/\epsilon )$. This scale is different from the Thouless localization length ${\lambda }_{\epsilon }\propto \ln (1/\epsilon )$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.

arXiv comment26 pages, LaTex, 9 PS figures included

References in corpus (8)

• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• Delocalization Transition via Supersymmetry in one Dimension
• Random Bonds and Topological Stability in Gapped Quantum Spin Chains
• Coexistence of antiferromagnetism and dimerization in a disordered spin-Peierls model: exact results
• Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics
• Comment on ``Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids''
• Enhanced magnetic fluctuations in doped spin-Peierls systems: a single-chain model analysis

Cited by in corpus (31)

• Single parameter scaling in one-dimensional localization revisited
• Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
• Single parameter scaling in 1-D Anderson localization. Exact analytical solution
• Thermal transport in one-dimensional spin gap systems
• Functionals of the Brownian motion, localization and metric graphs
• Spinor Slow-Light and Dirac particles with variable mass
• Exact Numerical Calculation of the Density of States of the Fluctuating Gap Model
• Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder
• Singularities and Pseudogaps in the Density of States of Peierls Chains
• Statistical properties of localisation--delocalisation transition in one dimension
• Some spectral properties of the one-dimensional Dirac equation
• Fluctuations of random matrix products and 1D Dirac equation with random mass
• Conductance of 1D quantum wires with anomalous electron-wavefunction localization
• Disorder-dressed quantum evolution
• Effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian
• Fluctuation effects in disordered Peierls systems
• Anomalous dimensions of operators without derivatives in the non-linear sigma-model for disordered bipartite lattices
• Thermodynamics of strongly disordered spin ladders
• From Disordered Quantum Walk to Physics of Off-diagonal Disorder
• One-Dimensional Disordered Supersymmetric Quantum Mechanics: A Brief Survey
• Breaking supersymmetry in a one-dimensional random Hamiltonian
• Localized and Extended States in One-Dimensional Disordered System: Random-Mass Dirac Fermions
• Large Spin Formation and Thermodynamic Properties of Disordered Spin Ladders with Site Dilution
• Microwave conductivity of a d-wave superconductor disordered by extended impurities: a real-space renormalization group approach
• Random-Mass Dirac Fermions in an Imaginary Vector Potential (I): Delocalization Transition and Localization Length
• Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length
• Bond-impurity induced bound states in disordered spin-1/2 ladders
• Quantum lattice Boltzmann study of random-mass Dirac fermions in one dimension
• A New Construction for Spinor Wave Equations
• Quantum Spin Chains with Nonlocally-Correlated Random Exchange Coupling and Random-Mass Dirac Fermions
• The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels