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arXiv:2312.08919 · Physical review. B./Physical review. B

Scaling and data collapse of two-dimensional random singlet states in a magnetic field

Chen Peng, Long Zhang

Published Jan 8, 2025• 3 citations
arXivHTMLPDF

Abstract

Quenched randomness strongly affects properties of magnetic materials. Two-dimensional (2D) random singlet (RS) states emerge in the random $J\text{\ensuremath{-}}Q$ model by destroying valence bond solid order with spatial randomness. We examine the 2D RS states in a magnetic field with quantum Monte Carlo simulations. The magnetization and susceptibilities show power-law scaling with magnetic field at low temperature. Moreover, they show one-parameter scaling behavior with $B/T$, and the scaling functions are remarkably consistent with a phenomenological model of random spin pairs with a singular distribution of interactions. These universal scaling functions can be used to diagnose 2D RS states in experiments.

DOI
10.1103/physrevb.111.014409

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Quenched randomness strongly affects properties of magnetic materials. Two-dimensional (2D) random singlet (RS) states emerge in the random J\ensuremath-QJ\text{\ensuremath{-}}QJ\ensuremath-Q model by destroying valence bond solid order with spatial randomness. We examine the 2D RS states in a magnetic field with quantum Monte Carlo simulations. The magnetization and susceptibilities show power-law scaling with magnetic field at low temperature. Moreover, they show one-parameter scaling behavior with B/TB/TB/T, and the scaling functions are remarkably consistent with a phenomenological model of random spin pairs with a singular distribution of interactions. These universal scaling functions can be used to diagnose 2D RS states in experiments.
Using quantum Monte Carlo simulations, we study effects of disorder on the S=1/2S=1/2S=1/2 Heisenberg model with exchange constant JJJ on the square lattice supplemented by multispin interactions QQQ. 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 rrr as ${r}^{\ensuremath{-}2}$, as in the one-dimensional RS state. The dynamic exponent $z\ensuremath{\ge}2$, 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 QQQ 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 zzz 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.
Abstract Recently measurements on various spin–1/2 quantum magnets such as H 3 LiIr 2 O 6 , LiZn 2 Mo 3 O 8 , ZnCu 3 (OH) 6 Cl 2 and 1T-TaS 2 —all described by magnetic frustration and quenched disorder but with no other common relation—nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C [ H , T ] in temperature T and magnetic field H exhibits T / H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling C [ H , T ]/ T ~ H − γ F q [ T / H ] with F q [ x ] = x q at small x , with q ∈ {0, 1, 2} an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a q -dependent subdominant term enforced by Maxwell’s relations.
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1/2 per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of YbMgGaO_{4}, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO_{4} and related materials.
In this work, we study the scaling relation of energy and length scales in the two-dimensional (2D) random singlet (RS) state in the random QQQ model. To investigate the intrinsic energy scale of the spinon subsystem arising from the model, we develop a constrained subspace update algorithm within the framework of the stochastic series expansion method to extract the singlet-triplet gap of the system. The 2D RS state exhibits scaling behavior similar to the infinite-randomness fixed point, at least within the length scales that we simulate. Furthermore, by rescaling the system size according to the strength of randomness, we observe that the data for the excitation gap and the width of the gap distribution collapse onto a single curve. This implies that a model with different strengths of randomness may correspond to the same fixed point.
We analyze the effect of quenched disorder on spin-1=2 quantum magnets in which magnetic frustration promotes the formation of local singlets.Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids.We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1=2 moments.This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations.Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1=2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate.Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1=2 per statistical unit cell.These conjectures are supported by an argument for 1D spin chains.We apply insights from this study to the phenomenology of YbMgGaO 4 , a recently discovered triangular lattice spin-1=2 insulator which was proposed to be a quantum spin liquid.We instead explore a description based on the present theory.Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO 4 and related materials.
Understanding disorder-induced exotic states in two-dimensional magnets is one of the central topics in the study of frustrated magnetism. Here, the authors focus on the randomness-induced disordered phase in the spin-\textonehalf{} ${J}_{1}\ensuremath{-}{J}_{2}$ square-lattice Heisenberg model with a strong bond randomness, by using large-scale density matrix renormalization group (DMRG) simulations. The results not only reveal the absent spin-glass order, but also identify the power-law decay of the average spin correlation and the exponential decay of the typical spin correlation. These all agree with the corresponding behavior in the one-dimensional random-singlet state and characterize the random-singlet nature of this disordered phase. This shows that DMRG simulations provide opportunities for exploring the disorder effect in two-dimensional magnets.