2D Subsystem Research Articles

Detecting subsystem symmetry protected topological order through strange correlators

We employ strange correlators to detect 2D subsystem symmetry-protected topological (SSPT) phases which are nontrivial topological phases protected by subsystem symmetries. Specifically, we analytically construct efficient strange correlators in the 2D cluster model in the presence of a uniform magnetic field and then perform the projector Quantum Monte Carlo simulation within the quantum annealing scheme. We find that strange correlators show the long-range correlation in the SSPT phase, from which we define strange order parameters to characterize the topological phase transition between the SSPT phase at low fields and the trivial paramagnetic phase at high fields. Thus, the detection of the fully localized zero modes on the 1D physical boundary of SSPT phase has been transformed into the bulk correlation measurement about the local operators with the periodic boundary condition. We also find interesting spatial anisotropy of a strange correlator, which can be intrinsically traced back to the nature of spatial anisotropy of subsystem symmetries that protect SSPT order in the 2D cluster model. By simulating strange correlators, we, therefore, provide the first unbiased large-scale quantum Monte Carlo simulation on the easy and efficient detection in the SSPT phase and open the avenue of the investigation of the subtle yet fundamental nature of the novel interacting topological phases.

Higher-order Weyl superconductors with anisotropic Weyl-point connectivity

Weyl superconductors feature Weyl points at zero energy in the three-dimensional (3D) Brillouin zone and arc states that connect the projections of these Weyl points on the surface. We report that higher-order Weyl superconductors can be realized in odd-parity topological superconductors with time-reversal symmetry being broken by periodic driving. Different from conventional Weyl points, the higher-order Weyl points in the bulk separate 2D first- and second-order topological phases, while on the surface, their projections are connected not only by conventional surface Majorana arcs, but also by hinge Majorana arcs. We show that the Weyl-point connectivity via Majorana arcs is largely enriched by the underlying higher-order topology and becomes anisotropic with respect to surface orientations. We identify the anisotropic Weyl-point connectivity as a characteristic feature of higher-order Weyl materials. As each 2D subsystem can be singled out by fixing the periodic driving, we propose how the Majorana zero modes in the 2D higher-order topological phases can be detected and manipulated in experiments.

Fractalizing quantum codes

We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms of well understood lower-dimensional spin models. Fractalization is also useful for deriving new spin models and quantum codes from known ones. We construct higher dimensional generalizations of fracton models that host extended fractal excitations. Finally, by applying fractalization to a 2D subsystem code, we produce a family of locally generated 3D subsystem codes that are conjectured to saturate a quantum information storage tradeoff bound.

Spectral weights of mixed coupled plasmon modes in Dirac electron systems with different dimensionality

Abstract We study the effects of coupling between plasmon modes by the long-range Coulomb electron–electron interaction for a system consisting of a two-dimensional (2D) system of Dirac electrons embedded in three-dimensional (3D) Dirac semimetal. We obtain the dispersions of coupled plasmon modes for various separations of the subsystems. The coupled modes become more separated with decreasing the separation between two subsystems as the coupling increases due to the enhanced Coulomb interaction between electrons from different subsystems. We also demonstrate how the coupling affects the spectral weights of the obtained modes in two subsystems for different separations. In the 2D subsystem both coupled modes have finite weights for small wave numbers, while for large wave numbers only the upper mode persists. On the other hand, in the bulk this mode takes most of the spectral weight for small wave numbers, while for large wave numbers the lower mode is more pronounced.

Optimal Periodic Control of Hypersonic Cruise Vehicle: Trajectory Features

Optimal periodic control is an effective technique to reduce aerodynamic heating and fuel consumption of hypersonic cruise vehicles. Herein, this optimal control problem has been solved by nonlinear programming and passed the posteriori check of optimality. The results indicate that the lift coefficient and velocity in dynamical model could be recognized as constants. Accordingly, the original 3D system consists of velocity, flight path angle, and altitude, which could be decoupled into a 2D subsystem and a 1D one. The 2D subsystem could describe the correlation between the flight path angle and altitude. And the period length is mainly dependent on the maximum altitude difference. The 1D subsystem has been proved to be feasible to describe the variation of kinetic energy or velocity. On basis of the subsystems, the heating and fuel performances of periodic cruise have been studied. The heating performance is mainly dependent on the maximum altitude difference, and the fuel consumption is mainly dependent on the drag coefficient. The features concluded in this paper can support rapid trajectory planning or suboptimal feedback design of hypersonic cruise vehicles.

Model Averaging and Input Transformation for 3D Needle Steering

In this paper, a duty-cycle-based method is proposed for needle steering in 3D. The paper models the continuous 3D needle steering problem as a four-mode switching system and provides a new average-based formulation to transform the continuous input into a switching sequence. In this structure, the needle tip deflection control system is decomposed to two different 2D subsystems. Each subsystem has its own input, for which a controller can be designed to adjust a switching duty cycle. The duty cycles from the two subsystems are then combined to provide an axial needle rotation command to control the needle deflection in 3D. In order to show the application of the proposed formulation, robust sliding mode technique is employed to design controllers for each subsystem and, thus for the total system in 3D. The controllers are designed to be robust with respect to uncertainties in the value of the needle path curvature and to deal with measurement limitations. The performance of the proposed framework is shown by performing experiments in different scenarios.

Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study.

We investigate geometric phase (GP) effects in nonadiabatic transitions through a conical intersection (CI) in an N-dimensional linear vibronic coupling (ND-LVC) model. This model allows for the coordinate transformation encompassing all nonadiabatic effects within a two-dimensional (2D) subsystem, while the other N - 2 dimensions form a system of uncoupled harmonic oscillators identical for both electronic states and coupled bi-linearly with the subsystem coordinates. The 2D subsystem governs ultra-fast nonadiabatic dynamics through the CI and provides a convenient model for studying GP effects. Parameters of the original ND-LVC model define the Hamiltonian of the transformed 2D subsystem and thus influence GP effects directly. Our analysis reveals what values of ND-LVC parameters can introduce symmetry breaking in the 2D subsystem that diminishes GP effects.

Subsystem codes with spatially local generators

We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both proportional to L. The gauge group of these codes involves only two-qubit generators of type XX and ZZ coupling nearest neighbor qubits (and some auxiliary one-qubit generators). Our proof is not constructive as it relies on a certain version of the Gilbert-Varshamov bound for classical codes. Along the way we introduce and study properties of generalized Bacon-Shor codes which might be of independent interest. Secondly, we prove that any 2D subsystem [n,k,d] code with spatially local generators obeys upper bounds kd=O(n) and d^2=O(n). The analogous upper bound proved recently for 2D stabilizer codes is kd^2=O(n). Our results thus demonstrate that subsystem codes can be more powerful than stabilizer codes under the spatial locality constraint.

Similarity transformation of matrices to one common canonical form and its applications to 2D linear systems

Similarity transformation of matrices to one common canonical form and its applications to 2D linear systemsThe notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the reduced 2D system is positive if and only if the linear transformation matrix is monomial. Necessary and sufficient conditions are established for the existence of a gain matrix such that the matrices of the closed-loop system can be reduced to the common canonical form.

Coexistance of spiral and commensurate structures in a triangular antiferromagnet KFe(MoO4)2

Magnetization, specific heat, magnetic resonance and neutron diffraction measurements are used to study the magnetic structure of KFe(MoO4)2. This stacked triangular antiferromagnet (TN=2.5 K) demonstrates an unusual breaking of the spin system into two intercalated and almost independent 2D subsystems. One is a collinear antiferromagnet with a simple spin-flop behavior. The other is a spiral magnet. The spin structure may be explained assuming two types of inequivalent magnetic planes with distorted triangular lattices of Fe3+(S=5/2) ions.

A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes

We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of size O(1). Our first result concerns the optimal scaling of the distance d with the linear size of the lattice L. We prove an upper bound d=O(LD-1) which is tight for D=1, 2. This bound applies to both subspace and subsystem stabilizer codes. Secondly, we analyze the suitability of stabilizer codes for building a self-correcting quantum memory. Any stabilizer code with geometrically local generators can be naturally transformed to a local Hamiltonian penalizing states that violate the stabilizer condition. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of the code. We prove that for D=1, 2, different logical states can be mapped into each other by a sequence of single-qubit Pauli errors such that the energy of all intermediate states is upper bounded by a constant independent of the lattice size L. The same result holds if there are unused logical qubits that are treated as ‘gauge qubits’. It demonstrates that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1, 2. This result is in sharp contrast with the existence of a classical self-correcting memory in the form of a two-dimensional (2D) ferromagnet. Our results leave open the possibility for a self-correcting quantum memory based on 2D subsystem codes or on 3D subspace or subsystem codes.

Acoustic modes in 2D atomic hydrogen on the surface of superfluid 4He

Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.

Polarization Induced Electronic Processes in a Quantum Well

Analysis of the electronic states in two dimensional systems is of considerable interest for the exclusive use of 2D systems in microelectronic devices as well as for the close relation of this problem to investigations of the some quantum effects. In microelectronic devices, the coupling between the electron 2D subsystem and polarization (induced or spontaneous) is often effectuated by depositing a lattice on the surface of a film with the 2D gas. In this case, the electrons are subjected to an external (or internal) periodic potential, which makes it possible to investigate the electron spectrum in such system. In present paper, the spectrum of the electronic states in an infinitely deep two dimensional asymmetric potential well, where one wall is periodically rough, is investigated theoretically. It is shown that in non-Bragg type resonances arise in such well. The resonances occur in a wide range of energies, starting at values close to the bottom in each 2D sub-band. The resonance interaction splits the energy spectrum and results in the appearance of gaps, giving the electron spectrum a mini-band character. The properties of the electron gas vary substantially in accordance with the new characteristics of the spectrum.