arXiv subjects

Jian-Te Wang

Publications and source records attributed to Jian-Te Wang.

8 recordsLinked to original sources

arXiv2026

Floquet quantum geometry in periodically driven topological insulators

Quantum geometry plays a fundamental role across many branches of modern physics, yet its full characterization in nonequilibrium systems remains a challenge. Here, we propose a framework for quantum geometry in Floquet topological insulators by introducing a time-resolved quantum metric tensor, defined via the trace distance between micromotion operators in momentum-time space. For class A in two spatial dimensions, we find a general inequality linking the Floquet quantum metric tensor and the Floquet topology: the associated quantum volume is bounded below by the Floquet topological invariant. This relation is found to also hold in class AIII in one dimension, where the Floquet geometric tensor may be notably reduced due to time-reflection symmetry. This work will be useful in digesting the general aspects of quantum geometry in periodically driven systems in connection with their topological characterization.

cond-mat.mes-hall↗

arXiv2024

Proposal for realizing and probing topological crystalline insulators in optical lattices

We develop a lattice model which exhibits topological transitions from $Z_2$ topological insulators to mirror symmetry-protected topological crystalline insulators by introducing additional spin-orbit coupling terms. The topological phase is characterized by the mirror winding number, defined within the mirror symmetry invariant subspace, which ensures the protection of gapless edge states and zero-energy corner states under specific boundary conditions. Additionally, we propose a feasible scheme using ultracold atoms confined in a stacked hexagonal optical lattice with Raman fields to realize the two-dimensional topological crystalline insulators. Detection of the mirror winding number in these systems can be achieved by implementing a simple quench sequence and observing the evolution of the time-of-flight patterns.

cond-mat.quant-gas↗

arXiv2024

Non-Abelian quantum geometric tensor in degenerate topological semimetals

The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian with global degenerate ground states, and give a general relation between the corresponding non-Abelian quantum metric and unit Bloch vector. This enables us to construct the relation between the non-Abelian quantum metric and Berry or Euler curvature. To be concrete, we present and study two topological semimetal models with global degenerate bands under CP and $C_2T$ symmetries, respectively. The topological invariants of these two degenerate topological semimetals are the Chern number and Euler class, respectively, which are calculated from the non-Abelian quantum metric with our constructed relations. Based on the adiabatic perturbation theory, we further obtain the relation between the non-Abelian quantum metric and the energy fluctuation. Such a non-adiabatic effect can be used to extract the non-Abelian quantum metric, which is numerically demonstrated for the two models of degenerate topological semimetals. Finally, we discuss the quantum simulation of the model Hamiltonians with cold atoms.

quant-ph↗

arXiv2024

Detecting degenerate bands topological invariants in optical lattice

In this paper, we present a novel experimental approach for simulating and detecting topological invariants using ultracold fermions confined in two-dimensional hexagonal optical lattices. We propose achieving two-fold degenerate four-band models with non-trivial topologies in both the AII and A classes by introducing additional inertial forces, Raman processes, or periodic driving. By implementing various quench sequences and observing the evolution of the time-of-flight pattern, we can gather comprehensive information about the ground states and determine the topology of the valence bands. Through the analysis of tomographic results, we are able to extract and calculate the spin Chern number for both spin-conserving and spin-nonconserving cases. Additionally, we demonstrate the robustness of the quantized topological invariants and discuss the effects of various experimental parameters.

cond-mat.quant-gas↗

arXiv2024

Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice

We propose a feasible scheme to realize a four-band Stiefel-Whitney insultor (SWI) with spin-orbit coupled ultracold atoms in an optical Raman lattice. Four selected spin states are coupled by carefully designed Raman lasers, to generate the desired spin-orbit interactions with spacetime inversion symmetry. We map out a phase diagram with respect to the experimental parameters, where a large topological phase region exists. We further present two distinct detection methods to resolve the non-abelian band topology, in both equilibrium and dynamical ways. The detection relies on the spin textures extracted from the time-of-flight imaging, showing the tomographic signatures in the ground states and long-time averaged patterns on certain submanifold via a bulk-surface duality. Our work paves a realistic way to explore novel real topology with quantum matters.

cond-mat.quant-gas↗

arXiv2023

Quantum quenches in a pseudo-Hermitian Chern insulator

We propose to uncover the topology of a pseudo-Hermitian Chern insulator by quantum quench dynamics. The Bloch Hamiltonian of the pseudo-Hermitian Chern insulator is defined in the basis of the q-deformed Pauli matrices, which are related to the representation of the deformed algebras. We show the bulk-surface duality of the pseudo-Hermitian phases, then further build a concrete relation between the static band topology and quench dynamics, in terms of the time-averaged spin textures. The results are also generalized into a fully nonequilibrium case where the postquench evolution is governed by a Floquet pseudo-Hermitian Hamiltonian. Furthermore, we propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.

cond-mat.mes-hall↗

arXiv2022

Damping transition in an open generalized Aubry-André-Harper model

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.

cond-mat.quant-gas↗

arXiv2022

Extracting non-Abelian quantum metric tensor and its related Chern numbers

The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space, based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.

quant-ph↗