Orbital Entropy Research Articles

Exploring Short-Range Correlations in symmetric nuclei: Insights into contacts and entanglement entropy

The Short-Range Correlations between nucleons in nuclei are regarded as a complex system. We investigate the relationship between the orbital entanglement entropy of SRCs Sij in nuclear structures and Tan contact cij, and find that the orbital entanglement entropies and Tan contacts corresponding to proton-proton SRC pairs and neutron-proton SRC pairs in nuclei demonstrate a scaling relation. More specifically, the proportionality of entanglement entropy between proton-proton pairs and neutron-proton pairs is directly related to the ratio of nuclear contacts within the atomic nucleus, demonstrating an approximate ratio of 2.0. Our research suggests that this scaling relationship should hold true for all symmetric nuclei, furthermore, we offer a possible explanation for this phenomenon.

Entanglement entropy between short range correlations and the Fermi sea in nuclear structure

The nuclear structure orbital entanglement entropy of short range correlation (SRC) is calculated based on the nuclear scale separation, specifically, the entanglement between the SRC orbitals and the rest of the system. It should be stressed that this is a single nucleon and not a pair entanglement entropy between the proton and neutron. The entanglement arises from the probability for a nucleon to occupy a momentum state above the Fermi momentum. The momentum space of the nucleus separates into two parts such that nucleons can occupy the mean-field part of the wave function, i.e., the Fermi sea (FS) and separately the high-momentum SRC part. The orbital entropy obtained is between these two parts where essentially two momentum subspaces are defined, one containing all the low momentum FS states and the other containing the high-momentum part as a SRC ``orbital'' state. For the calculation of the decoupling of low and high momenta which was established by the similarity normalization group the SRC is employed and viewed as a further orbital which can be multiply occupied. Since the probability of the occupation of a single SRC is given by the nuclear contact a simple general expression of the orbital entanglement entropy for SRC by employing the generalized contact formalism is obtained. This general formula for the SRC orbital entanglement entropy of a nuclear structure in terms of the nuclear contact allows one to obtain the scaling of the entropy in terms of the mass number, $A$. From this formula it is evident that, unlike the entanglement entropy of many quantum systems which scales with the surface area, the orbital entanglement entropy associated with the SRC in large nuclei is linearly dependent on $A$, i.e., it is shown to be extensive.

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in case of CI calculations reaches about 20 billion terms. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. The canonical wave functions/natural orbitals and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex non-equilibrium time-dependent process, induced nuclear fission described within a real-time Density Functional Theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short range correlations between fermions.

Prethermalization and entanglement dynamics in interacting topological pumps

We investigate the formation of quasisteady states in one-dimensional pumps of interacting fermions at non-integer filling fraction, in the regime where the driving frequency and interaction strength are small compared to the instantaneous single-particle band gap throughout the driving cycle. The system rapidly absorbs energy from the driving field, and approaches a quasisteady state that locally resembles a maximal entropy state subject to the constraint of fixed particle number in each of the system's single-particle Floquet bands. We explore the nature of this quasisteady state through one-body observables including the pumped current and natural orbital occupations, as well as the (many-body) entanglement spectrum and entropy. Potential disorder significantly reduces the amplitude of fluctuations of the quasisteady state current around its universal value, while the lifetime of the quasisteady state remains nearly unaffected for disorder strengths up to the scale of the single-particle band gap. Interestingly, the natural orbital occupations and entanglement entropy display patterns signifying the periodic entangling and disentangling of the system's degrees of freedom over each driving cycle. Moreover, prominent features in the system's time-dependent entanglement spectrum reveal the emergence of new long timescales associated with the equilibration of many-particle correlations.

The Shannon–McMillan–Breiman theorem beyond amenable groups

We introduce a new isomorphism-invariant notion of entropy for measure-preserving actions of arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy. It employs Danilenko’s orbital approach to entropy of a partition, and it is motivated by Seward’s recent generalization of Rokhlin’s characterization of entropy from amenable to general groups. A key ingredient in our approach is the use of an auxiliary probability-measure-preserving hyperfinite equivalence relation. Under the assumption of ergodicity of the auxiliary equivalence relation, our main result is a Shannon–McMillan–Breiman pointwise almost sure convergence theorem for the orbital entropy of partitions in measure-preserving group actions, the first such convergence result going beyond the realm of amenable groups. As a special case, we obtain a Shannon–McMillan–Breiman theorem for all strongly mixing actions of any countable group. Furthermore, we compare orbital Rokhlin entropy to Rokhlin entropy, and using an important recent result of Seward, we show that they coincide for free ergodic actions of any countable group. Finally, we consider actions of non-abelian free groups and demonstrate the geometric significance of the entropy equipartition property implied by the Shannon–McMillan–Breiman theorem. We show that the orbital entropy of a partition is the limit of the information functions of the sequence of partitions arising from refining any given finite partition along almost every horoball in the group.

Overlooked Transportation Anisotropies in d-Band Correlated Rare-Earth Perovskite Nickelates

Anisotropies in electronic transportations conventionally originate from the nature of low symmetries in crystal structures, and were not anticipated for perovskite oxides, the crystal asymmetricity of which is far below, e.g. van der Waals or topological crystal. Beyond conventional expectations, herein we demonstrate pronounced anisotropies in the inter-band coulomb repulsion dominated electronic transportation behaviors under low-dimensional confinement for the perovskite family of rare-earth nickelates (ReNiO3). From one aspect, imparting bi-axial interfacial strains upon various lattice planes results in extrinsic anisotropies in the abrupt orbital transitions of ReNiO3, and their metal to insulator transition behaviors that elevates the transition temperature beyond the existing merit. From the other aspect, the in-plane orbital entropy associated to the in-plane symmetry of the NiO6 octahedron within ReNiO3 causes intrinsic anisotropies for the gradually orbital transition with temperature to further improve their thermistor transportation properties. The present work unveils the overlooked role of the electronic orbital directionality within low dimensional correlated perovskites that can trigger anisotropic transportation behaviors, in spite of their relatively symmetric crystal structures. Establishing anisotropic transportations integrating the electron correlation and quantum confinement effects will bring in a new freedom for achieving further improvement in transportation properties of multi-functional perovskite oxides.

Matrix Liberation Process II: Relation to Orbital Free Entropy

AbstractWe investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.

Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer.

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO–LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose a complete active space. Moreover, the dependence of the ground-state energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

The topological entropy of non-dense orbits and generalized Schmidt games

We generalize the notion of Schmidt games to the setting of the general Caratheódory construction. The winning sets for such generalized Schmidt games usually have large corresponding Caratheódory dimensions (e.g., Hausdorff dimension and topological entropy). As an application, we show that for every $C^{1+\unicode[STIX]{x1D703}}$-partially hyperbolic diffeomorphism $f:M\rightarrow M$ satisfying certain technical conditions, the topological entropy of the set of points with non-dense forward orbits is bounded below by the unstable metric entropy (in the sense of Ledrappier–Young) of certain invariant measures. This also gives a unified proof of the fact that the topological entropy of such a set is equal to the topological entropy of $f$, when $f$ is a toral automorphism or the time-one map of a certain non-quasiunipotent homogeneous flow.

A remark on orbital free entropy

A lower estimate of the orbital free entropy $\chi_\mathrm{orb}$ under unitary conjugation is proved, and it together with Voiculescu's observation shows that the conjectural exact formula relating $\chi_\mathrm{orb}$ to the free entropy $\chi$ breaks in general in contrast to the case when given random multi-variables are all hyperfinite.

Study of entropic characteristics of strongly correlated systems using VO2 as a model case.

To explain the huge caloric effects often observed in the first-order electronic phase transition in the strongly correlated oxides, the entropic characteristics are investigated in VO2. By evaluating the spin and charge fluctuations based on the local moment model and the Sommerfeld coefficient in the high-temperature rutile phase, it is found that these fluctuations of the high-temperature phase are the main source of the entropic change during the transition. This mode of entropic change is realized by the quenching of these fluctuations owing to the formation of a singlet bonding state in the low-temperature monoclinic phase. By introducing oxygen deficiency, a vagueness in the gap at the Fermi level is confirmed by the transport data, the X-ray photoelectron spectra and also the electronic structure calculated by the first-principles calculations. In this case, the entropic feature at the transition is weakened. Consequently, the large caloric phenomena of the strongly correlated oxides are a result of the conversion of the internal energy gain owing to the orbital selection at the ground state into the free energy gain owing to the spin and charge fluctuations at finite temperature.

Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO π bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

Orbital ordering to orbital glass transition in spinel FeCr2−xAlxS4 (0 ⩽ x ⩽ 0.2)

The polycrystalline (PC) sample of FeCr2S4 displays orbital ordering around TOO ∼ 9 K, while single crystal sample shows orbital glass. In this paper, with the substitution of Al for Cr, a step by step transition from the orbital ordering to the orbital glass is reported in FeCr2−xAlxS4 (0 ⩽ x ⩽ 0.2). For PC FeCr2S4, the onset of long-range orbital order at TOO is evidenced by the appearance of a step-like transition in the temperature dependence of the magnetization (M(T)), a small kink at about 5.5 T below 9 K in the isotherms' magnetic field dependence of the magnetization (M(H)) curves as well as a λ-type anomaly in specific heat. With increasing Al content, the TOO decreases gradually. For the samples with x ⩾ 0.1, the orbital ordering is replaced by orbital glass, where the specific heat obeys a T2-dependence. The calculated residual orbital entropy consistently increases with x, implying the progressive freezing of the orbital moments and the coexistence of orbital ordering and orbital glass in the middle doping level.

Investigation of metal–insulator-like transition through theab initiodensity matrix renormalization group approach

We have studied the metal--insulator-like transition in pseudo-one-dimensional systems, i.e., lithium and beryllium rings, through the ab initio density matrix renormalization group (DMRG) method. Performing accurate calculations for different interatomic distances and using quantum information theory, we investigated the changes occurring in the wave function between a metallic-like state and an insulating state built from free atoms. We also discuss entanglement and relevant excitations among the molecular orbitals in the Li and Be rings and show that the transition bond length can be detected using orbital entropy functions. Also, the effect of different orbital bases on the effectiveness of the DMRG procedure is analyzed comparing the convergence behavior.

Investigations of the coupling of spin-orbital in MgTi2O4 by the magnetic entropy measurements

Single phase MgTi 2 O 4 compound was synthesized by spark plasma sintering (SPS) method. The temperature dependence of the magnetic susceptibility and specific heat measurements show that MgTi 2 O 4 takes place in phase transition at 258 K. Magnetic entropy measurements show that the change of magnetic entropy ΔSM is positive and ΔSM increases more quickly than H2/3 near the transition; while ΔSM is negative and |ΔSM| (the absolute value) increases slowly with applied field increasing at lower temperature. The change of ΔSM at different temperature range is suggested to be related not only to spin entropy change, but also orbital entropy change. The magnetic phases of MgTi 2 O 4 are suggested to be Pauli paramagnetic, collinear antiferromagnetic and non-collinear antiferromagnetic order with temperature decrease.

δ-doped LaAlO3-SrTiO3 interface: Electrical transport and characterization of the interface potential

Here we investigate the LaAlO3-SrTiO3 heterostructure with δ-doping of the interface by LaMnO3 at less than one monolayer. This doping strongly inhibits the formation of a mobile electron layer at the interface. This results in a giant increase of the resistance and the thermopower of the heterostructure. Several aspects of this phenomena are investigated. A model to calculate the carrier concentration is presented and the effect of doping with detailed temperature dependence is analyzed in terms of model parameters and weak-scattering theory. The large enhancement of the thermopower is attributed to the increased spin and orbital entropy originating from the LaMnO3 monolayer.

Competing electronic states in high temperature phase of NaTiO2

First principle density functional theory calculations on the high temperature phase of layered triangular lattice system NaTiO2 have revealed that a collective electronic state exists energetically close to the ground state but with competing transport properties: the latter is metallic with partially occupied doubly degenerate e′g orbitals, whereas the former is insulating with a1g orbital fully occupied. Significant occupation of this excited state is possible at non zero temperature either thermally or thanks to very soft (large amplitude) oxygen vibrations. Possible explanations of the experimental low conductivity based on competing orbital transport and of the specific heat jump at a structural transition based on orbital entropy are discussed.

Observation of the large magnetocaloric effect and suppression of orbital entropy change in Fe-doped MnV2O4

We present the structural and magnetic properties of Mn1−xFexV2O4 (x = 0.1, 0.2, and 0.3), and investigate the magnetocaloric effect in those compounds. The ferrimagnetic spin ordering is enhanced with the Fe doping at Mn site of MnV2O4, while the orbital ordering is suppressed. Large magnetic entropy changes up to 3.8 J/kg K as well as the relative cooling power up to 110 J/kg at the field change of 0-2 T for Mn1−xFexV2O4 are calculated from the isothermal magnetization measurements. The large orbital entropy change of MnV2O4 is suppressed by the Fe doping, while the spin entropy contribution arising from the strong spin-orbit coupling remains. Moreover, the doping of Fe broadens the temperature span of the large magnetic entropy change and increases the relative cooling power of MnV2O4 by 2.4 times.

Orbital free entropy, revisited

We give another definition of orbital free entropy introduced by Hiai, Miyamoto and us, which does not need the hyperfiniteness assumption for each given random multi-variable. The present definition is somehow related to one of its several recent `generalizations' due to Biane and Dabrowski, but completely agrees with the original definition and much closer to the original approach.

Concavification of free entropy

We introduce a modification of Voiculescu’s free entropy which coincides with the lim inf variant of Voiculescu’s free entropy on extremal states, but is a concave upper semi-continuous function on the trace state space. We also extend the orbital free entropy of Hiai et al. (2009) [8] to non-hyperfinite multivariables and prove freeness in the case of additivity of Voiculescu’s entropy (or vanishing of our extended orbital entropy).