Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Network Models in Class C on Arbitrary Graphs

We consider network models of quantum localisation in which a particle with a two-component wave function propagates through the nodes and along the edges of an arbitrary directed graph, subject to a random SU(2) rotation on each edge it traverses. The propagation through each node is specified by an arbitrary but fixed S-matrix. Such networks model localisation problems in class C of the classification of Altland and Zirnbauer [1], and, on suitable graphs, they model the spin quantum Hall transition. We extend the analyses of Gruzberg, Ludwig and Read [5] and of Beamond, Cardy and Chalker [2] to show that, on an arbitrary graph, the mean density of states and the mean conductance may be calculated in terms of observables of a classical history-dependent random walk on the same graph. The transition weights for this process are explicitly related to the elements of the S-matrices. They are correctly normalised but, on graphs with nodes of degree greater than 4, not necessarily non-negative (and therefore interpretable as probabilities) unless a sufficient number of them happen to vanish. Our methods use a supersymmetric path integral formulation of the problem which is completely finite and rigorous.     

Observables in 3d spinfoam quantum gravity with fermions

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.     

Generalized lattice gauge theory, spin foams and state sum invariants

We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the underlying manifold (≤3, ≤4, any). Ordinary LGT is recovered if the category is the (symmetric) category of representations of a compact Lie group. In the weak coupling limit we recover discretized BF-theory in terms of a coordinate-free version of the spin foam formulation. We work on general cellular decompositions of the underlying manifold.

In particular, we are able to formulate LGT as well as spin foam models of BF-type with quantum gauge group (in dimension ≤4) and with supersymmetric gauge group (in any dimension).

Technically, we express the partition function as a sum over diagrams denoting morphisms in the underlying category. On the LGT side this enables us to introduce a generalized notion of gauge fixing corresponding to a topological move between cellular decompositions of the underlying manifold. On the BF-theory side this allows a rather geometric understanding of the state sum invariants of Turaev/Viro, Barrett/Westbury and Crane/Yetter which we recover.

The construction is extended to include Wilson loop and spin network type observables as well as manifolds with boundaries. In the topological (weak coupling) case this leads to topological quantum field theories with or without embedded spin networks.     

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains

In quasi-one-dimensional(q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic(AFM) compound YbAlO_3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations,and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave(LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.     

Completeness of the classical 2D Ising model and universal quantum computation

We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.     

Ruelle resonances in kicked quantum spin chain

We study exponential decay of high temperature time correlation functions in a non-integrable quantum spin chain problem, namely Ising spin 1/2 chain kicked with tilted homogeneous magnetic field. For this purpose we define a master propagator over a suitable banach space of quantum observables (quantum many-body analogue of Perron–Frobenius operator) whose leading eigenvalue determines the asymptotic decay of correlations. This is demonstrated with explicit calculation for which a fast algorithm for the construction of the master propagator is developed.     

Quantum dynamics of tight-binding networks coherently controlled by external fields

With some reviews on the investigations on the schemes for quantum state transfer based on spin systems, we discuss the quantum dynamics of magnetically-controlled networks for Bloch electrons. The networks are constructed by connecting several tight-binding chains with uniform nearest-neighbor hopping integrals. The external magnetic field and the connecting hopping integrals can be used to control the intrinsic properties of the networks. For several typical networks, rigorous results are shown for some specific values of external magnetic field and the connecting hopping integrals: a complicated network can be reduced into a virtual network, which is a direct sum of some independent chains with uniform nearest-neighbor hopping integrals. These reductions are due to the fermionic statistics and the Aharonov-Bohm effects. In application, we study the quantum dynamics of wave packet motion of Bloch electrons in such networks. For various geometrical configurations, these networks can function as some optical devices, such as beam splitters, switches and interferometers. When the Bloch electrons as Gaussian wave packets input these devices, various quantum coherence phenomena can be observed, e.g., the perfect quantum state transfer without reflection in a Y-shaped beam, the multi-mode entanglers of electron wave by star-shaped network, magnetically controlled switches, and Bloch electron interferometer with the lattice Aharonov-Bohm effects. With these quantum coherent features, the networks are expected to be used as quantum information processors for the fermion system based on the possible engineered solid state systems, such as the array of quantum dots that can be implemented experimentally.      

Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension

We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g., energy) and include states with diverging correlation length and unbounded multiparticle entanglement. As a demonstration, we apply our approach to the Ising model on 1D, 2D, and 3D square lattices. We also present generalizations to higher spins and continuous-variable systems, which allows for the investigation of lattice field theories.     

A Proposal for a Bohmian Ontology of Quantum Gravity

The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a quantum theory of space-time and therefore focus on loop quantum gravity. We conceive atoms of space, represented in terms of nodes linked by edges in a graph, as the primitive ontology of the theory and show how a non-local law in which a universal and stationary wave-function figures can provide an order of configurations of such atoms of space such that the classical space-time of general relativity is approximated. Although there is as yet no fully worked out physical theory of quantum gravity, we regard the Bohmian approach as setting up a standard that proposals for a serious ontology in this field should meet and as opening up a route for fruitful physical and mathematical investigations.     

Neural-Network Quantum State of Transverse-Field Ising Model

Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355 (2017) 602], we construct the neural-network quantum state of transverse-field Ising model (TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration (SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.     

Wilson loops,geometric operators and fermions in 3d group field theory

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Quantum criticality of quantum speed limit for a two-qubit system in the spin chain with the Dzyaloshinsky–Moriya interaction

We study the quantum speed limit (QSL) time of a two-qubit system coupled to a spin–chain model with the Dzyaloshinsky–Moriya (DM) interaction. For the Bell state coupled to the Ising model or anisotropic XY model, we find that there is a prominent corresponding relationship between the QSL time and quantum phase transition in a spin–chain environment with larger scale, and the DM interaction can strongly enhance or suppress the response relation. Remarkably, when the surrounding environment is set to the XX model, the DM interaction makes it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point. In addition, our analyses indicate that the entanglement can speed-up the system evolution in many-body environment.     

Chiral metal as a ferromagnetic super spin chain

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low-energy spin states. The result is of a universal form and coincides with that for a hermitian random matrix.     

Path Integral Approach of Quantum Heisenberg Planar Spin Glass Model in the Presencesof Random Field

A quantum version of the site-random Heisenberg planar XY model in a random field is presented in the boson representation. Like classical spherical model in the spin space, the model can be solved exactly within the coherent state path integral-representation. The phase diagram is obtained, and the effects of the randomness and quantum fluctuations on the onset of a spin glass phase are discussed.     

Spin analysis of supersymmetric particles

The spin of supersymmetric particles can be determined at e⁺e^- colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles – smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in e⁺e^- collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza–Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an e⁺e^- collider.     

Quantum quench in the transverse-field Ising chain

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.