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.
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.
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.
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 $z\ensuremath{\ge}2$, 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 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.
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.
Abstract Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboard J-Q model by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergent O(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance, 1 / T 1 , exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature, 1 / T 1 rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas 1 / T 1 drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponent φ ≈ 0.3, consistent with the scaling ansatz ϕ = ν z with ν ≈ 0.3 and z = 1. Near the quantum phase transition, the temperature dependent 1 / T 1 shows a broad crossover regime where a universal scaling 1 / T 1 ∼ T η with η ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.
Abstract Quantum critical points (QCPs) ubiquitously emerge in strongly correlated systems, with their influence extending beyond zero temperature. There exist extended quantum critical regimes (QCRs) at finite temperatures and external fields. A paradigmatic example exhibiting QCP is quantum Ising magnets like CoNb 2 O 6 , where critical quantum fluctuations and robust universal scaling behavior provide crucial insights into the quantum material. In this work, we discover a fundamentally distinct quantum supercritical regime (QSR) emerging also from the QCP but controlled by symmetry-breaking fields (h) coupled to the order parameter. The QSR is enclosed by the crossover boundaries T~h zν/Δ , where z, ν and Δ≡β+γ are critical exponents. Amongst other intriguing phenomena, there exists an enhanced magnetocaloric effect (MCE) in QSR, characterized by a universally diverging magnetic Gr\"uneisen ratio Γ h ≡1/T(∂T/∂h) S ~T -Δ/zν . Even small symmetry-breaking fields generate dramatic temperature variations. The supercritical scaling can be comprehended via thermal data collapse based on the derived scaling form. We propose to observe the QSR and related supercritical MCE in CoNb 2 O 6 and other quantum Ising magnets, which may enable cryogenic technologies capable of reaching the millikelvin regime without relying on helium-3.