Quantum Spin Glass Research Articles

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases.

Dicke-model quantum spin and photon glass in optical cavities: Nonequilibrium theory and experimental signatures

In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a ``cavity glass microscope'' for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a ``photon glass'' state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function ${g}^{(2)}(\ensuremath{\tau})$.

Effect of quantum fluctuations on the coloring of random graphs

We present a study of the coloring problem (antiferromagnetic Potts model) of random regular graphs, submitted to quantum fluctuations induced by a transverse field, using the quantum cavity method and quantum Monte-Carlo simulations. We determine the order of the quantum phase transition encountered at low temperature as a function of the transverse field and discuss the structure of the quantum spin glass phase. In particular, we conclude that the quantum adiabatic algorithm would fail to solve efficiently typical instances of these problems because of avoided level crossings within the quantum spin glass phase, caused by a competition between energetic and entropic effects.

Collective strong coupling in multimode cavity QED

We study an atom-cavity system in which the cavity has several degenerate transverse modes. Mode-resolved cavity transmission spectroscopy reveals well-resolved atom-cavity resonances for several cavity modes, a signature of collective strong coupling for the different modes. Furthermore, the experiment shows that the cavity modes are coupled via the atomic ensemble contained in the cavity. The experimental observations are supported by a detailed theoretical analysis. The work paves the way to the use of interacting degenerate modes in cavity-based quantum information processing, where qubits corresponding to different cavity modes interact via an atom shared by the two modes. Our results are also relevant to the experimental realization of quantum spin glasses with ultracold atoms.

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

We derive the normal modes for a rotating Coulomb ion crystal in a Penning trap, quantize the motional degrees of freedom, and illustrate how they can be driven by a spin-dependent optical dipole force to create a quantum spin simulator on a triangular lattice with hundreds of spins. The analysis for the axial modes (oscillations perpendicular to the two-dimensional crystal plane) follow a standard normal-mode analysis, while the remaining planar modes are more complicated to analyze because they have velocity-dependent forces in the rotating frame. After quantizing the normal modes into phonons, we illustrate some of the different spin-spin interactions that can be generated by entangling the motional degrees of freedom with the spin degrees of freedom via a spin-dependent optical dipole force. In addition to the well-known power-law dependence of the spin-spin interactions when driving the axial modes blue of the phonon band, we notice certain parameter regimes in which the level of frustration between the spins can be engineered by driving the axial or planar phonon modes at different frequencies. These systems may allow for the analog simulation of quantum spin glasses with large numbers of spins.

Quantum Information and Statistical Mechanics: An Introduction to Frontier

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of quantum states, the so-called stabilizer states, and quantum operations on them. Furthermore, graph states, which are a class of stabilizer states associated with graphs, and their applications for measurement-based quantum computation are also mentioned. Based on the stabilizer formalism, we review two interdisciplinary topics. One is the relation between quantum error correction codes and spin glass models, which allows us to analyze the performances of quantum error correction codes by using the knowledge about phases in statistical models. The other is the relation between the stabilizer formalism and partition functions of classical spin models, which provides new quantum and classical algorithms to evaluate partition functions of classical spin models.

Dicke Quantum Spin Glass of Atoms and Photons

Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin-glass phase can appear, with a random linear combination of the cavity modes superradiant. We compute atomic and photon spectral response functions across this quantum phase transition, both of which should be accessible in experiments.

The Ground State Energy per Site of the Quantum and Classical Edwards-Anderson Spin Glass in the Thermodynamic Limit

We derive rigorous lower bounds for the average ground-state energy per site $e^{(d)}$ of the quantum and classical Edwards-Anderson spin-glass model in dimensions $d = 2$ and $d = 3$ in the thermodynamic limit. For the classical model they imply that $e^{(2)} \ge -3/2$ and $e^{(3)} \ge -2.204...$.

Quantum phase transitions and dynamical correlations in spin-glass systems

We study effects of random fluctuations in quantum spin-glass systems. We show that the expression of the magnetic susceptibility is divided into the classical and quantum parts. The former can be analyzed by the standard replica method with the static approximation. The latter incorporates dynamical correlations and is determined by the energy gap distribution. By using the many-body interacting Ising spin-glass model with transverse field, we discuss possible mechanisms of the quantum phase transitions.

Disordered Fermions on Lattices and Their Spectral Properties

We study Fermionic systems on a lattice with random interactions through their dynamics and the associated KMS states. These systems require a more complex approach compared with the standard spin systems on a lattice, on account of the difference in commutation rules for the local algebras for disjoint regions, between these two systems. It is for this reason that some of the known formulations and proofs in the case of the spin lattice systems with random interactions do not automatically go over to the case of disordered Fermion lattice systems. We extend to the disordered CAR algebra some standard results concerning the spectral properties exhibited by temperature states of disordered quantum spin systems. We investigate the Arveson spectrum, known to physicists as the set of the Bohr frequencies. We also establish its connection with the Connes and Borchers spectra, and with the associated invariants for such W ∗-dynamical systems which determine the type of von Neumann algebras generated by a temperature state. We prove that all such spectra are independent of the disorder. Such results cover infinite-volume limits of finite-volume Gibbs states, that is the quenched disorder for Fermions living on a standard lattice ℤ d , including models exhibiting some standard spin-glass-like behavior. As a natural application, we show that a temperature state can generate only a type $\mathop {\rm {III}}$ von Neumann algebra (with the type $\mathop {\rm {III_{0}}}$ component excluded). In the case of the pure thermodynamic phase, the associated von Neumann algebra is of type $\mathop {\rm {III_{\lambda }}}$ for some λ∈(0,1], independent of the disorder. All such results are in accordance with the principle of self-averaging which affirms that the physically relevant quantities do not depend on the disorder. The approach pursued in the present paper can be viewed as a further step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for the replicas.

Cluster fermionic Ising spin glass model with a transverse field

The fermionic Ising spin glass (SG) model in the presence of a transverse magnetic field Γ is studied within a cluster mean field theory. The model considers an infinite-range interaction among magnetic moments of clusters with a short-range ferromagnetic intracluster coupling J 0 . The spin operators are written as a bilinear combination of fermionic operators. In this quantum SG model, the intercluster disorder is treated by using a framework of one-step replica symmetry breaking (RSB) within the static approximation. The effective intracluster interaction is then computed by means of an exact diagonalization method. Results for several values of cluster size n s , Γ and J 0 are presented. For instance, the specific heat can show a broad maximum at a temperature T ∗ above the freezing temperature T f , which is characterized by the intercluster RSB. The difference between T ∗ and T f is enhanced by Γ , which suggests that the quantum effects can increase the ratio T ∗ / T f . Phase diagrams ( T versus Γ ) show that the critical temperature T f ( Γ ) decreases for any values of n s and J 0 when Γ increases until it reaches a quantum critical point at some value of Γ c .

Quantum simulation of frustrated Ising spins with trapped ions

A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social and neural networks to protein folding and magnetism. Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses. Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions, whose interactions are precisely controlled using optical forces. We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.

Energy-gap analysis of quantum spin-glass transitions at zero temperature

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass-paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear, spin-glass, and nonlinear susceptibilities. They diverge at different points, which we attribute to a quantum "Griffiths" mechanism. On the other hand, the classical treatment is justified for the transverse random energy model and the phase transition can be found by a sudden change of the ground state.

AKLT models with quantum spin glass ground states

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.

Effect of Random Fluctuations on Quantum Spin-Glass Transitions at Zero Temperature

We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad distributions of the energy gap. As a result, the linear, spin-glass, and nonlinear susceptibilities behave differently from each other. The power-law tail of the distribution implies a quantum Griffiths-like effect that could be observed in various random quantum systems. We also discuss the mechanisms of the phase transition in terms of the energy gap by comparing the Sherrington-Kirkpatrick model and random energy model, which demonstrate the difference between the continuous and discontinuous phase transitions.

Phase diagram of a short-range interacting SO(3) quantum spin-glass

We present a stable approximate solution for a quantum, short-range interacting, SO(3) Heisenberg disordered spin system on a square lattice, with a Gaussian distribution of couplings centered on an anti-ferromagnetic coupling J̄. The phase diagram T × J̄ contains a Néel (AF) phase at T = 0, J̄ > J̄0 and a spin-glass (SG) phase below a critical line, namely, T < Tc(J̄), J̄ < J̄0. The rest of the phase diagram is occupied by the paramagnetic (PM) phase.

Quantum spin glass relaxation in UCu4Ni

Strong non-exponential relaxation due to magnetic disorder in UCu4Ni is observed in zero- and longitudinal-field μSR measurements in this material. Zero-field experiments reveal no evidence for spin freezing down to 20 mK. Qualitatively the shape of the muon asymmetry curves in longitudinal fields is strongly affected as the field is increased from zero and less so as the field is increased towards kOe values. Analysis of the time/field scaling (t/Hγ) for the asymmetry data, performed without reference to any specific decay function or model, together with the absence of spin freezing enables one to classify this system as a quantum-spin-glass; i.e., similar to UCu4Pd. However, in contrast with the behavior of the Pd material and similarly to the more conventional spin glass AgMn, UCu4Ni follows (t/Hγ) scaling only above applied fields of order 100 Oe. Unlike UCu4Pd which has been discussed extensively as partially ordered, disorder ought to be randomly distributed in UCu4Ni.

Duality, quantum skyrmions, and the stability of a SO(3) two-dimensional quantum spin glass

Quantum topological excitations (skyrmions) are analyzed from the point of view of their duality to spin excitations in the different phases of a disordered two-dimensional, short-range interacting, SO(3) quantum magnetic system of Heisenberg type. The phase diagram displays all the phases, which are allowed by the duality relation. We study the large distance behavior of the two-point correlation function of quantum skyrmions in each of these phases and, out of this, extract information about the energy spectrum and non-triviality of these excitations. The skyrmion correlators present a power-law decay in the spin-glass(SG)-phase, indicating that these quantum topological excitations are gapless but nontrivial in this phase. The SG phase is dual to the AF phase, in the sense that topological and spin excitations are respectively gapless in each of them. The Berezinskii-Kosterlitz-Thouless mechanism guarantees the survival of the SG phase at $T \neq 0$, whereas the AF phase is washed out to T=0 by the quantum fluctuations. Our results suggest a new, more symmetric way of characterizing a SG-phase: one for which both the order and disorder parameters vanish, namely $<\sigma > = 0 $, $<\mu > =0 $, where $\sigma$ is the spin and $\mu$ is the topological excitation operators.

Replica symmetry breaking in a fermionic cluster spin glass model in a transverse field

Abstract We analyze a fermionic Ising spin glass model in the presence of a transverse magnetic field Γ within a cluster mean field theory. The model considers a Sherrington–Kirkpatrick type interaction between magnetic moments of clusters with a ferromagnetic intra-cluster coupling J 0 . The spin site operators are written as a bilinear combination of fermionic operators. In these quantum spin glass model, the inter-cluster disorder is treated by using a framework of one-step replica symmetry breaking within the static approximation. The effective intra-cluster interaction is then computed by means of an exact diagonalization method. Results for several cluster size n s , values of Γ and J 0 are presented. For instance, the specific heat shows a broad maximum (for n s > 1 ) at a temperature above the freezing temperature T f , which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T versus Γ show that the critical temperature T f ( Γ ) decreases for any value of n s when Γ increases until it reaches a quantum critical point at some value of Γ c .

On quantum spin glasses with finite connectivity: Cavity method and applications

We discuss quantum spin glasses with finite connectivity by presenting an extension of the cavity method used in studies of classical spin glasses.