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arXiv:1509.00704 · Physical review. B./Physical review. B

Disorder-induced enhancement and critical scaling of spontaneous magnetization in random-field quantum spin systems

Anindita Bera, Debraj Rakshit, Maciej Lewenstein, Aditi Sen, Ujjwal Sen, Jan Wehr

Published Jul 18, 2016• 11 citations
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Abstract

We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 $XY$ model, which magnetizes spontaneously in the absence of the random field. We adopt a mean-field approach for this analysis. In general, the models considered have Ising symmetry, and as such they exhibit ferromagnetic order in two and three dimensions in the presence of not too large disorder. Even in the special case when the model without disorder has $\text{U}(1)$ symmetry, a small $\text{U}(1)$-symmetry-breaking random field induces ferromagnetic long-range order in two dimensions. The mean-field approach, consequently, provides a rather good qualitative and even quantitative description when applied not too close to the criticality. We show that spontaneous magnetization persists even in the presence of the random field, but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained via analytical calculations within a perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of magnetization in the presence of the disorder field provided that we apply an additional constant field in the $XY$ plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the $XY$ spin system with arbitrary fixed quantum spin angular momentum.

DOI
10.1103/physrevb.94.014421

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We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 XYXYXY model, which magnetizes spontaneously in the absence of the random field. We adopt a mean-field approach for this analysis. In general, the models considered have Ising symmetry, and as such they exhibit ferromagnetic order in two and three dimensions in the presence of not too large disorder. Even in the special case when the model without disorder has U(1)\text{U}(1)U(1) symmetry, a small U(1)\text{U}(1)U(1)-symmetry-breaking random field induces ferromagnetic long-range order in two dimensions. The mean-field approach, consequently, provides a rather good qualitative and even quantitative description when applied not too close to the criticality. We show that spontaneous magnetization persists even in the presence of the random field, but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained via analytical calculations within a perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of magnetization in the presence of the disorder field provided that we apply an additional constant field in the XYXYXY plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the XYXYXY spin system with arbitrary fixed quantum spin angular momentum.
We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show by perturbative calculations and numerical simulations that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing and the magnetization at low- and high-temperature limits in the presence of disorder are estimated. Moreover, we treat the SO(n)n\mathrm{SO}(n) nSO(n)n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XYXYXY spin model in the presence of a constant magnetic field, in addition to the quenched disorder. We find that in the presence of the uniform magnetic field, disorder may enhance the component of magnetization in the direction that is transverse to the disordered field.
We investigate equilibrium statistical properties of the isotropic quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or annealed disorder or both. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales---the time scale associated with the equilibration of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We find that the magnetization survives in the presence of a unidirectional random field, irrespective of its nature, i.e., whether it is quenched or annealed. However, the field breaks the circular symmetry of the magnetization, and the system magnetizes in specific directions, parallel or transverse to the applied magnetic field. Interestingly, while the transverse magnetization is affected by the annealed disordered field, the parallel one remains unfazed by the same. Moreover, the annealed disorder present in the interaction term does not affect the system's spontaneous magnetization and the corresponding critical temperature, irrespective of the presence or absence of quenched or annealed disorder in the field term. We carry out a comparative study of these and all other different combinations of the disorders in the interaction and field terms, and point out their generic features.
We propose a general mechanism of random-field-induced order (RFIO), in which long-range order is induced by a random field that breaks the continuous symmetry of the model. We particularly focus on the case of the classical ferromagnetic XYXYXY model on a two-dimensional lattice, in a uniaxial random field. We prove rigorously that the system has spontaneous magnetization at temperature T=0T=0T=0, and we present strong evidence that this is also the case for small T>0T>0T>0. We discuss generalizations of this mechanism to various classical and quantum systems. In addition, we propose possible realizations of the RFIO mechanism, using ultracold atoms in an optical lattice. Our results shed new light on controversies in existing literature, and open a way to realize RFIO with ultracold atomic systems.
The LiHo_xY_{1-x}F_4 magnetic material in a transverse magnetic \nfield B_x perpendicular to the Ising spin direction has long been used \nto study tunable quantum phase transitions in pure and random disordered systems. \nWe first present analytical and numerical evidences for the validity of an effective spin-1/2 \napproach to the description of a general dipolar spin \nglass model with strong uniaxial Ising anisotropy and subject to weak \nB_x. \n We relate this toy model to the LiHo_xY_{1-x}F_4 transverse field Ising material. \n We show that an effective spin-1/2 \n model is able to capture both the qualitative and quantitative aspects of the \nphysics at small B_x. \nAfter confirming the validity of the effective spin-1/2 approach, we show that the field-induced magnetization along the \nx direction, \ncombined with the local random dilution-induced \ndestruction of crystalline mirror symmetries \ngenerates, via the predominant dipolar interactions between Ho^{3+} ions, \n random fields along the Ising z direction. \nThis identifies LiHo_xY_{1-x}F_4 in B_x as a new \nrandom field Ising system. \nWe show that the random fields explain the smearing \nof the nonlinear susceptibility at the spin glass transition \nwith increasing B_x. \nIn this thesis, we also investigate the phase diagram of non-diluted LiHoF_4 in the presence of B_x, by performing \nMonte-Carlo simulations. A previous quantum Monte Carlo (QMC) simulation found that even for small B_x where quantum fluctuations are small, close to the classical critical \npoint, there is a discrepancy between experiment and the QMC results. We revisit this problem, focusing on \nweak B_x close to the classical T_c, using an alternative approach. For small B_x, by applying a so-called cumulant \nexpansion, the quantum fluctuations around the classical T_c are taken into account perturbatively. We derived an effective \nperturbative classical Hamiltonian, on which MC simulations are performed. With this method we \ninvestigate different proposed sources of uncertainty which can affect the numerical results. \n We fully reproduce the previous QMC results at small B_x. Unfortunately, we find that \n none of the modifications to the microscopic Hamiltonian that we explore are able to provide a B_x-T phase diagram compatible with the experiments in the small \nsemi-classical B_x regime.
We calculate exactly the thermodynamics of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the critical region of the uniaxial spin-1/2 quantum chain. We derive a finite set of integral equations describing the complete temperature and magnetic field dependence of the system. Exact numerical results for arbitrary values of temperature and external magnetic field are obtained. We show that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with a critical non-Fermi-liquid behaviour of the magnetic susceptibility and specific heat. We point out that the `easy-plane' magnetic anisotropy does not qualitatively change the behaviour of the thermodynamic characteristics of the disordered impurities in the antiferromagnetic chain. On the other hand, anisotropy of ferromagnetic type can enhance the tendency to quenching of the impurities for strong disorder.
We propose a general mechanism of disorder-induced order by studying a particular case of classical ferromagnetic XY model in a random uniaxial field which breaks the continuous symmetry of the model. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical spin models and quantum systems. We propose a realization of this phenomenon with ultracold atoms in an optical lattice.