A ferromagnet in a continuously tunable random field

Quantum annealing of a frustrated magnet

Quantum annealing, which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet α-CoV2O6, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field. Below ~ 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field, but quickly converges towards that configuration with a nearly temperature-independent relaxation time of ~ 10 seconds in a transverse field of ~ 3.5 mK. Our many-body simulations show qualitative agreement with the experimental results, and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases, at low temperatures.

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Using high-precision Monte Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques, we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on a square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of a pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothing of the transition to second-order with the presence of strong scaling corrections.

Tuning high-Q nonlinear dynamics in a disordered quantum magnet

Quantum states cohere and interfere. Atoms arranged imperfectly in a solid rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent spin clusters by driving the system nonlinearly and measuring the resulting hole in the linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the Ising magnet LiHo0.045Y0.955F4, the quality factor Q for spectral holes can be as high as 100,000. We tune the dynamics by sweeping the Fano mixing parameter q through zero via the ac pump amplitude as well as a dc transverse field. The zero crossing of q is associated with a dissipationless response at the drive frequency. Identifying localized two-level systems in a dense and disordered magnet advances the search for qubit platforms emerging from strongly interacting, many-body systems.

Universality from disorder in the random-bond Blume-Capel model

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L^{*}≈32 for the chosen parameters.

Effect of random feld disorder on topological superconductors

We study the effect of random field disorder on two dimensional topological superconductors based on the Bogoliubov-de Gennes equations. A phase transition from the phase coherent state to the disordered state is identified numerically. The two phases can be characterized by two different correlation functions. In the phase coherent state, Majorana Fermion states form and may be influenced by the interaction between the vortex and the antivortex. The local density of states is calculated, which may be used to distinguish these two phases.

Random field disorder at an absorbing state transition in one and two dimensions

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.

Maximum-Entropy Inference with a Programmable Annealer

Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.

Using thermal boundary conditions to engineer the quantum state of a bulk magnet

The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter-sized crystals of the Ising magnet LiHo(x)Y(1-x)F4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.

Novel disordering mechanism in ferromagnetic systems with competing interactions

Ferromagnetic Ising systems with competing interactions are considered in the presence of a random field. We find that in three space dimensions the ferromagnetic phase is disordered by a random field which is considerably smaller than the typical interaction strength between the spins. This is the result of a novel disordering mechanism triggered by an underlying spin-glass phase. Calculations for the specific case of the long-range dipolar LiHo(x)Y(1-x)F(4) compound suggest that the above mechanism is responsible for the peculiar dependence of the critical temperature on the strength of the random field and the broadening of the susceptibility peaks as temperature is decreased, as found in recent experiments by Silevitch et al.. [Nature (London) 448, 567 (2007)]. Our results thus emphasize the need to go beyond the standard Imry-Ma argument when studying general random-field systems.

Random fields at a nonequilibrium phase transition

We study nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such random-field disorder is known to have dramatic effects: it prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we show that the phase transition of the one-dimensional generalized contact process persists in the presence of random-field disorder. The ultraslow dynamics in the symmetry-broken phase is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by large-scale Monte Carlo simulations.

Switchable hardening of a ferromagnet at fixed temperature

The intended use of a magnetic material, from information storage to power conversion, depends crucially on its domain structure, traditionally crafted during materials synthesis. By contrast, we show that an external magnetic field, applied transverse to the preferred magnetization of a model disordered uniaxial ferromagnet, is an isothermal regulator of domain pinning. At elevated temperatures, near the transition into the paramagnet, modest transverse fields increase the pinning, stabilize the domain structure, and harden the magnet, until a point where the field induces quantum tunneling of the domain walls and softens the magnet. At low temperatures, tunneling completely dominates the domain dynamics and provides an interpretation of the quantum phase transition in highly disordered magnets as a localization/delocalization transition for domain walls. While the energy scales of the rare earth ferromagnet studied here restrict the effects to cryogenic temperatures, the principles discovered are general and should be applicable to existing classes of highly anisotropic ferromagnets with ordering at room temperature or above.

Spin-glass transition at nonzero temperature in a disordered dipolar Ising system: the case of LiHoxY(1-x)F4

The physics of the spin-glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. In LiHoxY(1-x)F4, the Ho3+ moments, which are well described by Ising spins with only discrete "up or down" directions, interact predominantly via the inherently frustrated magnetostatic dipole-dipole interactions. The random frustration causing the SG behavior originates from the random substitution of dipole-coupled Ho3+ by nonmagnetic Y3+. In this Letter, we provide compelling evidence from extensive computer simulations that a SG transition at nonzero temperature occurs in a realistic microscopic model of LiHoxY(1-x)F4. This resolves the long-standing, and still ongoing, controversy about the existence of a SG transition in disordered dipolar Ising systems.

Quantum and classical glass transitions in LiHoxY1-xF4

When performed in the proper low-field, low-frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in a transverse field LiHo(x)Y(1-x)F(4) prove the existence of a spin-glass transition for x=0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.

Activated scaling of classical and quantum spin glasses

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a "critical rounding," chi(1) proportional to chi(3) proportional to [T ln(t/tau(0)')/K](gamma/b phi) exp - [Tt(g)(phi b)ln(t/tau(0)'/K)](nu/b) (T=temperature, t=time, K=barrier constant, t(g) = 1 - T(SG)/T, and T(SG) = transition temperature; gamma>0 for chi(3) and <0 for chi(1)). This model, also valid in the presence of resonant tunneling states at energies K(0) << K [provided that K is replaced by K(0)+2T ln (1/Gamma(0)), where Gamma(0)(2) proportional, variant tunnel splitting of a spin S=1], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system LiHo(x)Y(1-x) seems to follow this model.