Bogoliubov excitations in a Bose–Hubbard model on a hyperhoneycomb lattice

We study the topological properties of Bogoliubov excitation modes in a Bose–Hubbard model of three-dimensional(3 D)hyperhoneycomb lattices.For the non-interacting case,there exist nodal loop excitations in the Bloch bands.As the on-site repulsive interaction increases,the system is first driven into the superfluid phase and then into the Mott-insulator phase.In both phases,the excitation bands exhibit robust nodal-loop structures and bosonic surface states.From a topology point of view,these nodal-loop excitation modes may be viewed as a permanent fingerprint left in the Bloch bands.

State-Dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in Non-Hermitian Topological Systems with Generalized Inversion Symmetry

Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge states,but fail to describe the number and distribution of defective edge states in non-Hermitian topological systems.The state-dependent topological invariants,instead of a global topological invariant,are developed to accurately characterize the bulk-boundary correspondence of the NH systems,which is very different from their Hermitian counterparts.At the same time,we obtain the accurate phase diagram of the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with a generalized inversion symmetry from the state-dependent topological invariants.Therefore,these results will be helpful for understanding the exotic topological properties of various non-Hermitian systems.

Quantum critical duality in two-dimensional Dirac semimetals

Quantum criticality is closely related to the existence of two phases with unrelated symmetry breaking. In this paper,we study Néel and Kekulé valence bond state(VBS) quantum criticality in Dirac semimetals with four-fermion interactions.Our results show that all possible dynamical masses yield the same critical coupling, which exhibits the phenomenon that all possible phases meet at a multicritical point(e.g., a tricritical point for the Néel, Kekulé-VBS and semimetallic phases).In terms of the well-established Wess–Zumino–Witten field theory, we investigate the typical criticality for the transition between Néel and Kekulé-VBS phases, and the compatible Néel–Kekulé-VBS mass matrices imply the existence of a nonLandau transition between the Néel and Kekulé-VBS phases. We show the existence of mutual duality in the defect-driven Néel–Kekulé-VBS transition near the non-Landau critical point and find that this mutual duality results from the presence of a mutual Chern–Simons term. We also study the mutual duality based on dual topological excitations.

Collapses-revivals phenomena induced by weak magnetic flux in diamond chain

We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux(WMF),including Landau–Zener tunnelling,Bloch oscillations,localization phenomenon,and collapses-revivals phenomena.We observed that collapses-revivals phenomena can occur in diamond chain with WMF and cannot exist in the strong magnetic flux case as the previous study(Chang N N and Xue J K,2018,Chin.Phys.B 27105203).Induced by WMF,the energy band for the system varies from gapless to gapped structure.The position of the extrema of probability amplitude for ground state can also be altered by WMF within a single diamond plaquette.As a consequence,the transitions between different dynamical behaviors of bosons in diamond chain can be manipulated by WMF,depending on its initial configurations.

Emergent Quantum Dynamics of Vortex-Line under Linear Local Induction Approximation

Using the linear local induction approximation, we investigate the self-induced motion of a vortex-line that corresponds to the motion of a particle in quantum mechanics. Provided Kelvin waves, the effective Schr?dinger equation, physical quantity operators, and the corresponding path-integral formula can be obtained. In particular,the effective Planck constant defined by parameters of vortex-line motion shows the mathematical relation between the two fields. The vortexline–particle mapping may help in understanding particle motion in quantum mechanics.

Non-Hermitian Ising model at finite temperature

As a very simple model,the Ising model plays an important role in statistical physics.In the paper,with the help of quantum Liouvillian statistical theory,we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions.We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart.For example,the‘pseudo-phase transition’is explored between the‘topological’phase and the‘nontopological’phase,at which the Liouvillian energy gap is closed rather than the usual energy gap.In particular,we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field.This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

An exactly solvable model for two-dimensional non-Hermitian quasicrystals

The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson localization has been extended to many fields of physics,including the quasiperiodic or incommensurate systems.