Heisenberg Field Research Articles

Entanglement and quantum phase transition of spin glass: A renormalization group approach

Abstract Using a renormalization group approach, we study the entanglement properties of two spin glass models: the XXZ Heisenberg (with Dzyaloshinskii–Moriya interaction) and Ising transverse field spin glasses. The concurrence for both models are obtained through the Kadanoff renormalization group (RG) approach with random J i z and J i respectively. The constant couplings in the RG flow are randomized through the Gaussian distribution. For Δ = 0 corresponding to a non-spin glass material, a first-order transition is expected. By varying Δ from 0.05 to 0.5, the spin glass effect broadens the sharp transition resulting in a second-order-like transition. The fluctuations in the average concurrence for the spin glass case as measured by the standard deviations is also a good indicator of quantum phase transition.

Solvable Models in the Conventional and Light-Front Field Theory: Recent Progress

We discuss a few new results within the exactly solvable relativistic models studied in both the conventional and the light front field theory. The models include the Rothe–Stamatescu, the Thirring, the Federbush and the Thirring–Wess model. The unifying feature is that the corresponding field equations are solved in a simple and exact form. We work within the hamiltonian framework and pay a careful attention to the correct definition of interacting currents which are built from the known solutions in a point-split regularized manner. Quantum “anomalies” follow immediately. The Hamiltonians of the models are expressed in terms of the correct (dynamically independent) field variables, namely the free Heisenberg fields. Due to the simplicity of the models’ dynamics, one can explicitly determine structure of the physical ground states.

Boundary effects on quantum entanglement and its dynamics in a detector-field system

In this paper we analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. Firstly a set of coupled equations for the detector's and the field's Heisenberg operators are derived. Then we introduce the linear entropy as a measure of entanglement between the detector and the quantum field under mirror reflection, and solve the early-time detector-field entanglement dynamics. After coarse-graining the field, the dynamics of the detector's internal degree of freedom is described by a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded Green's functions and Hadamard elementary functions of the free quantum field in a half space. At late times when the combined system is in a stationary state, we obtain exact expressions for the detector's covariance matrix and show that the detector-field entanglement decreases for smaller separation between the detector and the mirror. We explain the behavior of detector-field entanglement qualitatively with the help of a detector's mirror image, compare them with the case of two real detectors and explain the differences.

Hamiltonian formulation of exactly solvable models and their physical vacuum states

We study simple two-dimensional models with massless and massive fermions in the Hamiltonian framework. While our ultimate goal is to gain a deeper insight to structural differences between the usual (“spacelike” – SL) and light-front (LF) forms of the relativistic dynamics, an attempt is also made to clarify a few conceptual problems of quantum field theory. We point out that contrary to the assumption of canonical quantization, interacting Heisenberg fields do not always reduce to free fields at t=0. We also show that by incorporating operator solutions of the field equations to the canonical formalism, SL and LF Hamiltonians of the derivative-coupling model as well as of the Federbush model acquire an equivalent structure. In the usual canonical treatment, physical predictions in the two schemes disagree – the SL Hamiltonians contain interaction terms while their LF counterparts do not. Using a Bogoliubov transformation, the physical vacuum of the Thirring model is then derived for the first time. It has a form of a coherent state quadratic in composite boson operators which, after bosonization of the vector current, are present in the (nondiagonal) interaction Hamiltonian. To find the vacuum of the Federbush model by an analogous Bogoliubov transformation, we propose a massive version of Klaiberʼs current bosonization and demonstrate advantages of the LF treatment of the model.

Galois Actions on the Eigenproblem of the Heisenberg Heptagon

We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field ℚ of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant. These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices.

Interpenetrating Three-Dimensional Diamondoid Lattices and Antiferromagnetic Ordering (Tc = 73 K) of MnII(CN)2

Thermolysis of either the 3-D, bridged-layered [NEt(4)]Mn(II)(3)(CN)(7) or 2-D, layered [NEt(4)](2)Mn(II)(3)(CN)(8) forms Mn(II)(CN)(2). Rietveld analysis of the high-resolution synchrotron powder X-ray diffraction data determined that Mn(II)(CN)(2) is cubic [a = 6.1488(3) Å] (space group = Pn3m) consisting of two independent, interpenetrating networks having the topology of the diamond lattice. Each tetrahedrally coordinated Mn(II) is bonded to four orientationally disordered cyanide ligands. Mn(II)(CN)(2) magnetically orders as an antiferromagnet with a T(c) = 73 K determined from the peak in d(χT)/dT. Exchange coupling estimated via the mean field Heisenberg model from the transition temperature (J/k(B) = -4.4 K) and low temperature magnetic susceptibility of the ordered phase (J/k(B) = -7.2 K) indicate that Mn(II)(CN)(2) experiences weak antiferromagnetic coupling. The discrepancy between those estimates is presumably due to local anisotropy at the Mn(II) sites arising from the CN orientational disorder or interactions between the interpenetrating lattices.

Study of the first-order phase transition in the classical and quantum random field Heisenberg model on a simple cubic lattice

The phase diagram of the Heisenberg ferromagnetic model in the presence of a magnetic random field (we have used bimodal distribution) of spin S=1/2 (quantum case) and S=∞ (classical case) on a simple cubic lattice is studied within the framework of the effective-field theory in finite cluster (we have chosen N=2 spins). Integrating out the part of order parameter (equation of state), we obtained an effective Landau expansion for the free energy written in terms of the order parameter Ψ(m). Using the Maxwell construction we have obtained the phase diagram in the T−H plane for all intervals of the field. The first-order transition temperature is calculated by the discontinuity of the magnetization at Tc∗(H), on the other hand in the continuous transition the magnetization is null at T=Tc(H). At null temperature (T=0) we have found the coexistence field Hc=3.23 J that is independent of spin value. The transition temperature Tc(H) for the classical case (S=∞), in the T−H plane, is larger than the quantum case (S=1/2).

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (−W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. First, what class of multitime averages the −W approximates and, second, how to proceed if the average in question does not belong to this class. To answer the first question, we develop a (in principle, exact) path-integral approach in phase space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The −W equations emerge as an approximation within these path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages, Kubo’s renowned formula relating the linear-response function to two-time commutators suffices. The −W is directly generalized to the response properties of the system allowing one to calculate approximate time normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

One-loop results for kink and domain wall profiles at zero and finite temperature

Using dimensional regularization, we compute the one-loop quantum and thermal corrections to the profile of the bosonic ($1+1$)-dimensional ${\ensuremath{\varphi}}^{4}$ kink, the sine-Gordon kink, and the $C{P}^{1}$ kink, and higher-dimensional ${\ensuremath{\varphi}}^{4}$ kink domain walls. Starting from the Heisenberg field equation in the presence of the nontrivial kink background we derive analytically results for the temperature-dependent mean field which display the onset of the melting of kinks as the system is heated towards a symmetry-restoring phase transition. The result is shown to simplify significantly when expressed in terms of a self-consistently defined thermal screening mass. In the case of domain walls, we find infrared singularities in the kink profile, which corresponds to interface roughening depending on the system size. Finally we calculate the energy density profile of ${\ensuremath{\varphi}}^{4}$ kink domain walls and find that in contrast to the total surface tension the local distribution requires composite operator renormalization in $3+1$ dimensions.

Spectral function of spinless fermions on a one-dimensional lattice

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density-matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, we show that 85% of the total spectral weight in the zero field Heisenberg model near wave-vector $q=\ensuremath{\pi}$ is given by the two-spinon contribution.

Finite-temperature lineshapes in gapped quantum spin chains

We consider the finite-temperature dynamical susceptibility $\ensuremath{\chi}(\ensuremath{\omega},q,T)$ of gapped quantum spin chains such as the integer spin Heisenberg and transverse field Ising models. At zero temperature $\ensuremath{\chi}$ in these models is dominated by a delta-function line arising from the coherent propagation of single-particle modes. Using methods of integrable quantum field theory, we determine the evolution of the lineshape at low temperatures. We show that the lineshape is in general asymmetric in energy. We discuss the application of our results to inelastic neutron-scattering experiments on gapped spin chain systems such as ${\text{Y}}_{2}{\text{BaNiO}}_{5}$ and ${\text{CsNiCl}}_{3}$.

N-quantum approach to quantum field theory at finite T and μ: the NJL model

We extend the N-quantum approach to quantum field theory to finite temperature ( T) and chemical potential ( μ) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized thermal Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2) f ⊗ SU(3) c version of the model can lead to a lowering of the vacuum energy density. We discuss how to go beyond the mean field approximation by including higher order terms in the Haag expansion.

Study of a Model of Quantum Electrodynamics

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model when the Hamiltonian is expressed in terms of the ``physical'' fields that create the electron together with its cloud of soft photons the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the ``physical'' field can be chosen to act in the space of the exact (``physical'') electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space.

2D topological solitons in the gauged easy-axis Heisenberg antiferromagnet model

Field equations of the 3-component U(1) gauged sigma model (“the A3M model”) with spontaneously broken Z (2) symmetry are presented for ( D + 1)-dimensional space-time. Localized solutions of the two-dimensional A3M model with the unit topological charge are found numerically; these topological solitons describe (at least for small values of a parameter p, p < p 0) stable bound states of the unit 3-component “easy-axis” Heisenberg field and the Maxwell field. Possible physical implications of 2D and 3D topological solitons of the A3M model are discussed.

The classical limit of ultralocal scalar fields

The classical limit of the quantum theory of ultralocal scalar fields is approached with the help of coherent state techniques. In the limit ℏ→0, it is demonstrated that the coherent state expectation value of the Heisenberg field operators coincide with the solutions of the corresponding classical canonical equations of motion.

Critical fluctuations of sums of weakly dependent random vectors

LetSn be sums of iid random vectors taking values in a Banach space andF be a smooth function. We study the fluctuations ofSn under the transformed measurePn given byd Pn/d P=exp (nF(Sn/n))/Zn. If degeneracy occurs then the projection ofSn onto the degenerate subspace, properly centered and scaled, converges to a non-Gaussian probability measure with the degenerate subspace as its support. The projection ofSn onto the non-degenerate subspace, scaled with the usual order\(\sqrt {n,} \) converges to a Gaussian probability measure with the non-degenerate subspace as its support. The two projective limits are in general dependent. We apply this theory to the critical mean field Heisenberg model and prove a central limit type theorem for the empirical measure of this model.

The vacuum for an interacting scalar field

We define a vacuum for a real scalar field interacting with a time-dependentc-number source which vanishes rapidly in the remote past and future. We then show that this vacuum is a more appropriate vacuum for the interacting field than the vacuum for the incoming Heisenberg field in the sense that the energy of the field is lower in the vacuum we propose as compared to the energy of the field in the vacuum for the incoming Heisenberg field.

Magnetismus von Europium-Clustern in intermetallischen Verbindungen mit Magnesium Teil 2 Über den Einfluβ von Aluminium auf die Intra- und Intercluster-Wechselwirkungen in Eu(Mg 1− xAl x) 5,2

The magnetic susceptibilities of the phases Eu(Mg 1− x Al x ) 5.2 with x=0.05 and 0.10 (which crystallize with a EuMg 5.2-type structure containing triangular Eu(4f 7) clusters) have been determined between 3.2 and 295 K. In the temperature range 40–295 K where the compounds obey the Curie-Weiss law with μ≈8.1 μ B , in contrast with EuMg 5.2, the paramagnetic Curie temperatures Θ p decrease from 7 K (EuMg 5.2) to 4.5 K ( x=0.05) or 0.5 K ( x=0.10). Below 40 K characteristic deviations from the Curie-Weiss straight line occur which on the basis of the Heisenberg and molecular field models allow the separation of intra- and intercluster exchange interactions. Within the triangular clusters the interaction is ferromagnetic whereas the intercluster effect is antiferromagnetic. The change in Θ p values with increasing aluminium content, tending towards an increase in antiferromagnetic contributions, results from a reduction in the ferromagnetic intracluster coupling and a strengthening of the antiferromagnetic intercluster effect.

Covariant formulation of multiple localized quantum measurements.

We have considered the dynamics of simple measuring devices coupled to quantized relativistic Heisenberg fields. We have defined localized observables and derived covariant equations for the joint probability distribution of the measured outcomes. The proposed formalism is based on standard field-theoretical terms. We have shown that our formalism yields the expected anticoincidence when two devices detect two wave packets of a single electron. Applications in the measurement theory of vacuum fluctuations have been suggested.

Fermionic and bosonic scattering phases on a topological kink

A general approach to the scattering of fundamental fermions and bosons on a topological kink excitation is considered. An asymptotic LSZ-analysis for secondary quantized Heisenberg fields and kink motion is developed and some new results for the phases of one-particle matrix elements for the elastic scattering on the kink are derived.