Heisenberg Field Research Articles

Anti-Instability of Complex Ghost

Abstract We argue that Lee–Wick’s complex ghost appearing in any higher derivative theory is stable and its asymptotic field exists. It may be more appropriate to call it “anti-unstable”, in the sense that the more the ghost "decays" into lighter ordinary particles, the larger the probability that the ghost remains as itself becomes. This is explicitly shown by analyzing the two-point functions of the ghost Heisenberg field which is obtained as an exact result in the N → ∞ limit in a massive scalar ghost theory with light O(N)-vector scalar matter. The anti-instability is a consequence of the fact that the poles of the complex ghost propagator are located on the physical sheet in the complex plane of four-momentum squared. This should be contrasted with the case of the ordinary unstable particle, whose propagator has no pole on the physical sheet.

Phase transitions, KMS condition and decision making: an introductory model.

We consider a simple model of interacting agents asked to choose between 'yes' and 'no' to some given question. The agents are described in terms of spin variables, and they interact according to a mean field Heisenberg model. We discuss under which conditions the agents can come out with a common choice. This is made using, in a social context, the notion of KMS states and phase transitions. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

WAVE PROPAGATION AND MAGNETIC ORDERING IN FERROMAGNETIC MATERIALS

The soliton wave solutions to the (2+1)-dimensional Heisenberg ferromagnetic spin chain [Formula: see text] problem are explored in this paper. The (2+1)-dimensional [Formula: see text] equation describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains in the semiclassical limit. This formula is based on the spin-chain of the Heisenberg field. The bilinear and anisotropic interactions are accounted for in this equation. Even ferromagnetism may be explained by this paradigm, since it describes the propagation of waves inside a substance (the magnetic ordering in ferromagnetic materials). To construct a new soliton wave solution and validate its correctness, modern analytical and approximative schemes are utilized such as the Khater II and Adomian decomposition methods. Numerous interpretations for solitary waves are shown by various plots such as polar plots, contour plots, two-dimensional plots, and three-dimensional plots. The study’s novelty may be appreciated by contrasting our findings with those presented in previously published research publications. Most of the many computational simulations used are performed with the aid of a program called Mathematica 13.1.

Bath-induced delocalization in interacting disordered spin chains

Over a decade of work has culminated in the consensus that one-dimensional systems, subject to sufficiently large disorder, fail to thermalize and possess an extensive set of local integrals of motion. In this Letter, I will provide numerical evidence for the contrary. In particular, this work studies the dynamics of disordered spin chains which are weakly coupled to a Markovian bath. Within this approach, the critical disorder for stability to quantum avalanches exceeds ${W}^{*}\ensuremath{\gtrsim}20$ in the random field Heisenberg chain. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime.

Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature.

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

Trends of information backflow in disordered spin chains

We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complementary part) to the system-qubit. A connection between environmental interruption caused by the information backflow and the disorder strength is established by examining the entanglement revival frequencies. The growth patterns of the revival frequencies in the localized phase plays an instrumental role to effectively distinguish an interacting system (many-body localized) from its non-interacting (Anderson localized) counterpart.

Kinetic Theory of Boson Gas

We construct a quantum kinetic theory of a weakly interacting critical boson gas using the expectation values of products of Heisenberg field operators in the grand canonical ensemble. Using a functional representation for the Wick theorem for time-ordered products, we construct a perturbation theory for the generating functional of these time-dependent Green’s functions at a finite temperature. We note some problems of the functional-integral representation and discuss unusual apparent divergences of the perturbation expansion. We propose a regularization of these divergences using attenuating propagators. Using a linear transformation to variables with well-defined scaling dimensions, we construct an infrared effective field theory. We show that the structure of the regularized model is restored by renormalization. We propose a multiplicatively renormalizable infrared effective model of the quantum dynamics of a boson gas.

Berry–Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs

An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the difference of the exchangeable pair is not bounded by a small deterministic constant, the error bound is often not optimal. In this paper, using the exchangeable pair approach of Stein's method, a new Berry-Esseen bound for an arbitrary random variable is established without a bound on the difference of the exchangeable pair. An optimal convergence rate for normal and non-normal approximation is achieved when the result is applied to various examples including the quadratic forms, general Curie-Weiss model, mean field Heisenberg model and colored graph model.

Evolution of Magneto-Orbital order Upon B-Site Electron Doping in Na_{1-x}Ca_{x}Mn_{7}O_{12} Quadruple Perovskite Manganites.

We present the discovery and refinement by neutron powder diffraction of a new magnetic phase in the Na_{1-x}Ca_{x}Mn_{7}O_{12} quadruple perovskite phase diagram, which is the incommensurate analogue of the well-known pseudo-CE phase of the simple perovskite manganites. We demonstrate that incommensurate magnetic order arises in quadruple perovskites due to the exchange interactions between A and B sites. Furthermore, by constructing a simple mean field Heisenberg exchange model that generically describes both simple and quadruple perovskite systems, we show that this new magnetic phase unifies a picture of the interplay between charge, magnetic, and orbital ordering across a wide range of compounds.

Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

Exploring many-body localization and thermalization using semiclassical methods

The Discrete Truncated Wigner Approximation (DTWA) is a semi-classical phase space method useful for the exploration of Many-body quantum dynamics. In this work we investigate Many-Body Localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a 1D random field Heisenberg spin chain with short range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long range interactions and/or systems in higher dimensions.

Efficient Representation of Fully Many-Body Localized Systems Using Tensor Networks

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of $\ell$ contiguous sites. We argue this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.

Operator entanglement entropy of the time evolution operator in chaotic systems

We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized and Floquet systems. In the random field Heisenberg model we find a universal power law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases. In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value). We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent-Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL and Floquet properties as the original Hamiltonian. The scaling and saturation properties reflect the spreading of the state EE of the corresponding time evolution. We conclude that the EE of the evolution operator should characterize the propagation of information in these systems.

Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians.

A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.

Anomalous Thermalization in Ergodic Systems.

It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.

Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach.

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.

Analysis of quantum spin models on hyperbolic lattices and Bethe lattice

The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.

Solvable Models with Massless Light-Front Fermions

Two-dimensional models with massless fermions (Thirring model, Thirring–Wess and Schwinger model, among others) have been solved exactly a long time ago in the conventional (space-like) form of field theory and in some cases also in the conformal field theoretical approach. However, solutions in the light-front form of the theory have not been obtained so far. The primary obstacle is the apparent difficulty with light-front quantization of free massless fermions, where one half of the fermionic degrees of freedom seems to “disappear” due to the structure of a non-dynamical constraint equation. We shall show a simple way how the missing degree of freedom can be recovered as the massless limit of the massive solution of the constraint. This opens the door to the genuine light front solution of the above models since their solvability is related to free Heisenberg fields, which are the true dynamical variables in these models. In the present contribution, we give an operator solution of the light front Thirring model, including the correct form of the interacting quantum currents and of the Hamiltonian. A few remarks on the light-front Thirring–Wess models are also added. Simplifications and clarity of the light-front formalism turn out to be quite remarkable.

Evidence for 3D isotropic long range spin-spin interaction near the ferromagnetic transition in bulk and thin film SrRuO3

In the case of metallic ferromagnets there has always been a controversy, i.e. whether the magnetic interaction is itinerant or localized. For example SrRuO3 is known to be an itinerant ferromagnet where the spin–spin interaction is expected to be mean field in nature. However, it is reported to behave like Ising, Heisenberg or mean field by different groups. Despite several theoretical and experimental studies and the importance of strongly correlated systems, the experimental conclusion regarding the type of spin–spin interaction in SrRuO3 is lacking. To resolve this issue, we have investigated the critical behaviour in the vicinity of the paramagnetic–ferromagnetic phase transition using various techniques on polycrystalline as well as (001) oriented SrRuO3 films. Our analysis reveals that the application of a scaling law in the field-cooled magnetization data extracts the value of the critical exponent only when it is measured at H → 0. To substantiate the actual nature without any ambiguity, the critical behavior is studied across the phase transition using the modified Arrott plot, Kouvel–Fisher plot and M–H isotherms. The critical analysis yields self-consistent β, γ and δ values and the spin interaction follows the long-range mean field model. Further the directional dependence of the critical exponent is studied in thin films and it reveals the isotropic nature. It is elucidated that the different experimental protocols followed by different groups are the reason for the ambiguity in determining the critical exponents in SrRuO3.

Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space $\mathit {F^{\otimes \frac{1}{2}}}$F⊗12

We construct the bosonization of the Fock space \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12 of a single neutral fermion by using a 2-point local Heisenberg field. We decompose \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12 as a direct sum of irreducible highest weight modules for the Heisenberg algebra \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}_{\mathbb {Z}}$\end{document}HZ, and thus we show that under the Heisenberg \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}_{\mathbb {Z}}$\end{document}HZ action the Fock space \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12 of the single neutral fermion is isomorphic to the Fock space \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes 1}}$\end{document}F⊗1 of a pair of charged free fermions, thereby constructing the boson-fermion correspondence of type D-A. As a corollary we obtain the Jacobi identity equating the graded dimension formulas utilizing both the Heisenberg and the Virasoro gradings on \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12. We construct a family of 2-point-local Virasoro fields with central charge \documentclass[12pt]{minimal}\begin{document}$-2+12\lambda -12\lambda ^2, \ \lambda \in \mathbb {C}$\end{document}−2+12λ−12λ2,λ∈C, on \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12. We construct a W1 + ∞ representation on \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12 and show that under this W1 + ∞ action \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes \frac{1}{2}}}$\end{document}F⊗12 is again isomorphic to \documentclass[12pt]{minimal}\begin{document}$\mathit {F^{\otimes 1}}$\end{document}F⊗1.