2020/06/25 by Lu Liu, Wenan Guo, Anders W. Sandvik · 17 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Critical exponent #Excited state #Exponent #Ground state #Heisenberg model #Ising model #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Randomness #Scaling #Singlet state #Spin (aerodynamics) #Spinon #Square lattice #Statistical physics #Statistics #Thermodynamic limit #Thermodynamics #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.054443
published in Physical review. B./Physical review. B 102(5) (American Physical Society) · 15 pages, 8 figures
arxiv created 2020/06/25 · openalex created_date 2020/07/02 · openalex publication_date 2020/08/31 · arxiv updated 2020/09/09 · openalex updated_date 2026/08/06
Using quantum Monte Carlo simulations, we study effects of disorder on the S=1/2 Heisenberg model with exchange constant J on the square lattice supplemented by multispin interactions Q. It was found recently [L. Liu et al., Phys. Rev. X 8, 041040 (2018)] that the ground state of this J\ensuremath-Q model with random couplings undergoes a quantum phase transition from the N'eel antiferromagnetic state into a randomness-induced spin-liquid-like state that is a close analog to the well known random-singlet (RS) state of the Heisenberg chain with random couplings. This 2D RS state arises from a spontaneously symmetry-broken fourfold degenerate columnar valence-bond solid that is broken up by the disorder into finite domains, with spinons localized at topological defects. The interacting spinons form a critical collective many-body state without magnetic long range order but with the mean spin-spin correlations decaying with distance r as r^\ensuremath-2, as in the one-dimensional RS state. The dynamic exponent z\ensuremath≥2, varying continuously with the model parameters. In this work, we further investigate the properties of the RS state in the J\ensuremath-Q model with random Q couplings. We study the temperature dependence of the specific heat and various susceptibilities for large enough systems to reach the thermodynamic limit. We also analyze the size dependence of the critical magnetic order parameter and its susceptibility in the ground state. For all these quantities, we find consistency with the conventional quantum-critical scaling laws when the condition implied by the r^\ensuremath-2 form of the spin correlations is imposed. In particular, all the different quantities can be explained by the same value of the dynamic exponent z at fixed model parameters. We argue that the RS state identified in the J\ensuremath-Q model corresponds to a generic renormalization group fixed point that can be reached in many quantum magnets with random couplings and that it has already been observed experimentally.