Renormalization group study of random quantum magnets

Abstract

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time N*log(N), independently of the topology of the graph and we went up to N~4*10^6. We have studied regular lattices with dimension D<=4 as well as Erdos-Renyi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and the ferromagnetic phases and generalized the numerical algorithm for another random quantum systems.

12 pages, 12 figures

References in corpus (12)

• Griffiths phases on complex networks
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Phase transition of one dimensional bosons with strong disorder
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ as a random field Ising ferromagnet
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Disorder induced rounding of the phase transition in the large q-state Potts model
• Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain
• Random walk in a two-dimensional self-affine random potential : properties of the anomalous diffusion phase at small external force

Cited by in corpus (49)

• Strong Disorder RG approach - a short review of recent developments
• Entanglement entropy dynamics of disordered quantum spin chains
• Random transverse-field Ising chain with long-range interactions
• Rare region effects in the contact process on networks
• Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Long-range random transverse-field Ising model in three dimensions
• Spectral analysis and slow spreading dynamics on complex networks
• Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• Slow, bursty dynamics as the consequence of quenched network topologies
• Long-range epidemic spreading in a random environment
• Rare regions of the Susceptible Infected Susceptible model on Barabási-Albert networks
• Localization transition, Lifschitz tails and rare-region effects in network models
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Reentrant Random Quantum Ising Antiferromagnet
• Infinite randomness critical behavior of the contact process on networks with long-range connections
• Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder
• Emergence of disconnected clusters in heterogeneous complex systems
• Strong Disorder RG principles within a fixed cell-size real space renormalization : application to the Random Transverse Field Ising model on various fractal lattices
• Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass
• Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature
• Extreme statistics of the excitations in the random transverse Ising chain
• Random Transverse Field Ising model in $d=2$ : analysis via Boundary Strong Disorder Renormalization
• Dynamics of Ising models near zero temperature : Real Space Renormalization Approach
• Random Transverse Field Ising model on the Cayley Tree : analysis via Boundary Strong Disorder Renormalization
• Infinite-disorder critical points of models with stretched exponential interactions
• Transverse-spin correlations of the random transverse-field Ising model
• Random quantum Ising model with three-spin couplings
• Three-dimensional quantum Griffiths singularity in bulk iron-pnictide superconductors
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow
• Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models
• Slow dynamics of the contact process on complex networks
• Multipartite Entanglement in the Random Ising Chain
• Scaling of local persistence in the disordered contact process
• Numerical evidences of a universal critical behavior of 2D and 3D random quantum clock and Potts models
• Random geometry at an infinite-randomness fixed point
• Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Manifestation of interdot spin tunneling effects in ordered arrays of quantum dots: An anomalous magnetization of In_{1-x}Mn_xAs
• Geometry of rare regions behind Griffiths singularities in random quantum magnets
• Random transverse and longitudinal field Ising chains
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
• Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal
• Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain