Crossover effects in the random exchange spin-1/2 antiferromagnetic chain

Abstract

The random antiferromagnetic spin-1/2 XX and XXZ chain is studied numerically for varying strength of the disorder, using exact diagonalization and stochastic series expansion methods. The spin-spin correlation function as well as the stiffness display a clear crossover from the pure behavior (no disorder) to the infinite randomness fixed point or random singlet behavior predicted by the the real space renormalization group. The crossover length scale is shown to diverge as $\xi \sim {\mathcal{D}}^{-\gamma }$, where $\mathcal{D}$ is the variance of the random bonds. Our estimates for the exponent $\gamma$ agrees well within the error bars with the one for the localization length exponent emerging within an analytical bosonization calculation. Exact diagonalization and stochastic series expansion results for the string correlation function are also presented.

13 pages, 15 figures, submitted to Phys. Rev. B

References in corpus (25)

• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• The superconductor-insulator transition in 2D dirty boson systems
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Persistent Currents in 1D Disordered Rings of Interacting Electrons
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Critical behavior of the S=3/2 antiferromagnetic Heisenberg chain
• Directed Loop Updates for Quantum Lattice Models
• Dynamics and transport in random quantum systems governed by strong-randomness fixed points
• Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets
• Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains
• Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
• Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains
• Numerical renormalization-group study of spin correlations in one-dimensional random spin chains
• Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain
• Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain
• Ground state of the random-bond spin-1 Heisenberg chain
• Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2 Chains
• Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"
• Scaling of the spin stiffness in random spin-1/2 chains : Crossover from pure-metallic behaviour to random singlet-localized regime
• Disorder Induced Phases in Higher Spin Antiferromagnetic Heisenberg Chains
• Comment on "Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2 Chains"
• Magnetic ordering in a doped frustrated spin-Peierls system
• Density matrix renormalization group analysis of the spin 1/2 XXZ chain in an XY symmetric random magnetic field
• Spin correlation functions in random-exchange s=1/2 XXZ chains

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• Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid
• Entanglement spectrum and entangled modes of random XX spin chains
• Quantum channels in random spin chains
• Bond disorder and breakdown of ballistic heat transport in the spin-1/2 antiferromagnetic Heisenberg chain as seen in Ca-doped SrCuO2
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings
• Valence Bond Entanglement and Fluctuations in Random Singlet Phases
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• Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
• Adaptive Density Matrix Renormalization Group for Disordered Systems
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Random free-fermion quantum spin chain with multi-spin interactions
• Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions
• Dynamics of weakly coupled random antiferromagnetic quantum spin chains
• Entanglement entropy and localization in disordered quantum chains
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
• Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers
• Witnessing Disorder in Quantum Magnets
• Renormalization-group investigation of the S=1 random antiferromagnetic Heisenberg Chain