Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study

Abstract

The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent $z>1$, which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing $z<1$, when the dynamics of the rare regions is hampered by the longitudinal field.

13 pages, 10 figures

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Cited by in corpus (26)

• Strong Disorder RG approach - a short review of recent developments
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Automatic structural optimization of tree tensor networks
• Calculation of higher-order moments by higher-order tensor renormalization group
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Entanglement renormalization for disordered systems
• Entanglement bipartitioning and tree tensor networks
• Reentrant Random Quantum Ising Antiferromagnet
• Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions
• Mixed-order transition in the antiferromagnetic quantum Ising chain in a field
• Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Ground-state energy distribution of disordered many-body quantum systems
• Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Random Ising chain in transverse and longitudinal fields: Strong disorder RG study
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings
• Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain
• Quantum Monte Carlo study of the bond- and site-diluted transverse-field Ising model
• Pattern Description of Quantum Phase Transitions in the Transverse Antiferromagnetic Ising Model with a Longitudinal Field
• Quantum Potts chain in alternating field
• Entanglement-based tensor-network strong-disorder renormalization group
• Random transverse and longitudinal field Ising chains