Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain

Abstract

Strong-Disorder Renormalization Group (SDRG), despite being a relatively simple real-space renormalization procedure, provides in principle exact results on the critical properties at the infinite-randomness fixed point of random quantum spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities of finite chains that are inaccessible to SDRG. In this work, the accuracy of this approach is studied and two simple and fast improvements are proposed. The accuracy on the ground state energy is improved by a factor at least equal to 4 for the random Ising chain in a transverse field. Finally, the proposed algorithms are shown to yield Binder cumulants of the 3-color random Ashkin-Teller chain that are compatible with a second-order phase transition while a first-order one is predicted by the original MPO-RG algorithm.

References in corpus (21)

• The density-matrix renormalization group
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement renormalization
• Strong disorder RG approach of random systems
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases
• Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
• Disorder induced cross-over effects at quantum critical points
• Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization
• Numerical renormalization-group study of spin correlations in one-dimensional random spin chains
• Self-assembling tensor networks and holography in disordered spin chains
• Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points
• Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Rounding of a first-order quantum phase transition to a strong-coupling critical point
• Entanglement renormalization for disordered systems
• Bond disorder induced criticality of the three-color Ashkin-Teller model
• Strong-randomness infinite-coupling phase in a random quantum spin chain
• Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

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• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models