Showing papers on "Ising model published in 2015"

Evidence for two-dimensional Ising superconductivity in gated MoS2

Abstract: The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

Two Dimensional Ising Superconductivity in Gated MoS$_{2}$

Abstract: The Zeeman effect, which is usually considered to be detrimental to superconductivity, can surprisingly protect the superconducting states created by gating a layered transition metal dichalcogenide. This effective Zeeman field, which is originated from intrinsic spin orbit coupling induced by breaking in-plane inversion symmetry, can reach nearly a hundred Tesla in magnitude. It strongly pins the spin orientation of the electrons to the out-of-plane directions and protects the superconductivity from being destroyed by an in-plane external magnetic field. In magnetotransport experiments of ionic-gate MoS$_{2}$ transistors, where gating prepares individual superconducting state with different carrier doping, we indeed observe a spin- protected superconductivity by measuring an in-plane critical field $\textit{B}$$_{c2}$ far beyond the Pauli paramagnetic limit. The gating-enhanced $\textit{B}$$_{c2}$ is more than an order of magnitude larger compared to the bulk superconducting phases where the effective Zeeman field is weakened by interlayer coupling. Our study gives the first experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

Crystallization in Ising quantum magnets

Abstract: Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. Here, we report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Our results demonstrate the precise control of Rydberg many-body systems and may enable future studies of phase transitions and quantum correlations in interacting quantum magnets.

Scaling and Universality at Dynamical Quantum Phase Transitions.

Abstract: Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.

Variational principle for steady states of dissipative quantum many-body systems.

Abstract: We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the dynamics. We show how to apply this approach to different classes of variational quantum states and demonstrate its successful application to a dissipative extension of the Ising model, which is of importance to ongoing experiments on ultracold Rydberg atoms, as well as to a driven-dissipative variant of the Bose-Hubbard model. Finally, we identify several advantages of the variational approach over previously employed mean-field-like methods.

Conformal invariance of spin correlations in the planar Ising model

Abstract: We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.

A Course on Large Deviations With an Introduction to Gibbs Measures

Abstract: Large deviations: General theory and i.i.d. processes Introductory discussion The large deviation principle Large deviations and asymptotics of integrals Convex analysis in large deviation theory Relative entropy and large deviations for empirical measures Process level large deviations for i.i.d. fields Statistical mechanics Formalism for classical lattice systems Large deviations and equilibrium statistical mechanics Phase transition in the Ising model Percolation approach to phase transition Additional large deviation topics Further asymptotics for i.i.d. random variables Large deviations through the limiting generating function Large deviations for Markov chains Convexity criterion for large deviations Nonstationary independent variables Random walk in a dynamical random environment Appendixes: Analysis Probability Inequalities from statistical mechanics Nonnegative matrices Bibliography Notation index Author index General index

Bootstrapping the Three Dimensional Supersymmetric Ising Model.

Abstract: We implement the conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the operator product expansion of a chiral and an antichiral primary, we find a kink at the expected location of the critical three dimensional N=2 Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory, as well as the stress-tensor two-point function. We find that the latter is in an excellent agreement with an exact computation.

Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes

Abstract: We show that a strongly interacting chain of Majorana zero modes exhibits a supersymmetric quantum critical point corresponding to the c=7/10 tricritical Ising model, which separates a critical phase in the Ising universality class from a supersymmetric massive phase. We verify our predictions with numerical density-matrix-renormalization-group computations and determine the consequences for tunneling experiments.

Efficiently Learning Ising Models on Arbitrary Graphs

Abstract: graph underlying an Ising model from i.i.d. samples. Over the last fifteen years this problem has been of significant interest in the statistics, machine learning, and statistical physics communities, and much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models. Nevertheless, for learning Ising models on general graphs with p nodes of degree at most d, it is not known whether or not it is possible to improve upon the pd computation needed to exhaustively search over all possible neighborhoods for each node.In this paper we show that a simple greedy procedure allows to learn the structure of an Ising model on an arbitrary bounded-degree graph in time on the order of p2. We make no assumptions on the parameters except what is necessary for identifiability of the model, and in particular the results hold at low-temperatures as well as for highly non-uniform models. The proof rests on a new structural property of Ising models: we show that for any node there exists at least one neighbor with which it has a high mutual information.

Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe.

Abstract: Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments.

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Abstract: The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.

Reexamining classical and quantum models for the D-Wave One processor

Abstract: We revisit the evidence for quantum annealing in the D-Wave One device (DW1) based on the study of random Ising instances. Using the probability distributions of finding the ground states of such instances, previous work found agreement with both simulated quantum annealing (SQA) and a classical rotor model. Thus the DW1 ground state success probabilities are consistent with both models, and a different measure is needed to distinguish the data and the models. Here we consider measures that account for ground state degeneracy and the distributions of excited states, and present evidence that for these new measures neither SQA nor the classical rotor model correlate perfectly with the DW1 experiments. We thus provide evidence that SQA and the classical rotor model, both of which are classically efficient algorithms, do not satisfactorily explain all the DW1 data. A complete model for the DW1 remains an open problem. Using the same criteria we find that, on the other hand, SQA and the classical rotor model correlate closely with each other. To explain this we show that the rotor model can be derived as the semiclassical limit of the spin-coherent states path integral. We also find differences in which set of ground states is found by each method, though this feature is sensitive to calibration errors of the DW1 device and to simulation parameters.

Long-range Ising and Kitaev models: phases, correlations and edge modes

Abstract: We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance r as , as well as a related class of fermionic Hamiltonians that generalize the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents α, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for , while connected correlation functions can decay with a hybrid exponential and power-law behavior, with a power that is α-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every α. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough α. For the fermionic models we show that the edge modes, massless for , can acquire a mass for . The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

Random Currents and Continuity of Ising Model’s Spontaneous Magnetization

Abstract: The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin model on $${\mathbb{Z}^d}$$ in d = 3 dimensions. The analysis also applies to higher dimensions, for which the result is already known, and to systems with interactions of power law decay. The proof employs in an essential way an extension of the Ising model’s random current representation to the model’s infinite volume limit. Using it, we relate the continuity of the magnetization to the vanishing of the free boundary condition Gibbs state’s long range order parameter. For reflection positive models the resulting criterion for continuity may be established through the infrared bound for all but the borderline lower dimensional cases. The exclusion applies to the one dimensional model with 1/r 2 interaction for which the spontaneous magnetization is known to be discontinuous at T c .

Quantum Criticality of Hot Random Spin Chains

Abstract: We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of $\mathrm{SU}(2{)}_{k}$ anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them ``quantum critical glasses.'' We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $k\ensuremath{\rightarrow}\ensuremath{\infty}$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.

Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

Abstract: It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.

Universal Features of Left-Right Entanglement Entropy.

Abstract: We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.

Quenches and dynamical phase transitions in a nonintegrable quantum Ising model

Abstract: We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagnetic interactions in the presence of a longitudinal field which renders the model nonintegrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field. Analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the nonanalyticities of the rate function of the return probability. Even though the model is nonintegrable, there are periodic occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP, while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.

Conformal Bootstrap With Slightly Broken Higher Spin Symmetry

Abstract: We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents $\gamma_s$ with large spin $s$. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.

Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

Abstract: Many-body localization in an $XY$ model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power law distance dependent hopping $V(R) \propto R^{-\alpha}$ always leads to the localization breakdown in a thermodynamic limit of an infinite system at $\alpha < 3d/2$ where $d$ is a system dimension. The delocalization takes place due to the induced Ising interactions $U(R) \propto R^{-2\alpha}$ of "extended" resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in $XY$ model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring $\alpha \geq 2d$ which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.

24.3 20k-spin Ising chip for combinational optimization problem with CMOS annealing

Abstract: In the near future, the performance growth of Neumann-architecture computers will slow down due to the end of semiconductor scaling. Presently a new computing paradigm, so-called natural computing, which maps problems to physical models and solves the problem by its own convergence property, is expected. The analog computer using superconductivity from D-Wave [1] is one of those computers. A neuron chip [2] is also one of them. We proposed a CMOS-type Ising computer [3]. The Ising computer maps problems to an Ising model, a model to express the behavior of magnetic spins (the upper left diagram in Fig. 24.3.1), and solves the problems by ground-state search operations. The energy of the system is expressed by the formula in the diagram. Computing flows are expressed in the lower flow chart in Fig. 24.3.1. In the conventional Neumann architecture, the problem is sequentially and repeatedly calculated, and therefore, the number of computing steps drastically increases as the problem size grows. In the Ising computer, in the first step, the problem is mapped to the Ising model. In the next steps, an annealing operation, the ground-state search by interactions between spins, are activated and the state transitions to the ground state where the energy of the system is minimized. The interacting operation between spins is decided by the interaction coefficients, which are set to each connection. Here, the configuration of the interaction coefficients is decided by the problem, and therefore, the interaction coefficients are equivalent to the programming in the conventional computing paradigm. The ground state corresponds to the solution of the original problem, and the solution is acquired by observing the ground state. The interactions for the annealing are performed in parallel, and the necessary steps for the annealing are smaller than that used by a sequential computing, Neumann architecture. As the table in Fig. 24.3.1, our Ising computer uses CMOS circuits to express the Ising model, and acquires the scalability and operation at room temperature.

Phase diagram of the interacting Majorana chain model

Abstract: The Hubbard and spinless fermion chains are paradigms of strongly correlated systems, very well understood using the Bethe ansatz, density matrix renormalization group (DMRG), and field theory/renormalization group (RG) methods. They have been applied to one-dimensional materials and have provided important insights for understanding higher-dimensional cases. Recently, an interacting fermion model has been introduced, with possible applications to topological materials. It has a single Majorana fermion operator on each lattice site and interactions with the shortest possible range that involve four sites. We present a thorough analysis of the phase diagram of this model in one dimension using field-theory/RG and DMRG methods. It includes a gapped supersymmetric region and a gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. In addition to a first-order transition, three critical points occur: tricritical Ising, Lifshitz, and a generalization of the commensurate-incommensurate transition. We also survey various gapped phases of the system that arise when the translation symmetry is broken by dimerization and find both trivial and topological phases with 0, 1, and 2 Majorana zero modes bound to the edges of the chain with open boundary conditions.

Topological Characterization of Extended Quantum Ising Models.

Abstract: We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic $XY$ model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the $XY$ model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.

Model reduction by manifold boundaries

Abstract: Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce “black boxes” disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees offreedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically “compressed” into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions.

M-theoretic matrix models

Abstract: Some matrix models admit, on top of the usual ’t Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N . These models, which we call M-theoretic matrix models, appear in the localization of Chern-Simons-matter theories, and also in two-dimensional statistical physics. Generically, their partition function receives non-perturbative corrections which are not captured by the ’t Hooft expansion. In this paper, we discuss general aspects of these type of matrix integrals and we analyze in detail two different examples. The first one is the matrix model computing the partition function of $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory in three dimensions with one adjoint hypermultiplet and N f fundamentals, which has a conjectured M-theory dual, and which we call the N f matrix model. The second one, which we call the polymer matrix model, computes form factors of the 2d Ising model and is related to the physics of 2d polymers. In both cases we determine their exact planar limit. In the N f matrix model, the planar free energy reproduces the expected behavior of the M-theory dual. We also study their M-theory expansion by using Fermi gas techniques, and we find non-perturbative corrections to the ’t Hooft expansion.