Related papers: Spontaneous Chern-Euler Duality Transitions
We study the dynamical quantum phase transition of the critical quantum quench, in which the prequenched Hamiltonian, or the postquenched Hamiltonian, or both of them are set to be the critical points of equilibrium quantum phase…
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking…
Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
According to the topological band theory of a Hermitian system, the different electronic phases are classified in terms of topological invariants, wherein the transition between the two phases characterized by a different topological…
In commonly employed models for 2D topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to…
The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena -- topological phases and…
The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the…
Continuous quantum phase transitions that are beyond the conventional paradigm of fluctuations of a symmetry breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band…
We point out that a fermion determinant of a chiral gauge theory on a 2D torus has a phase ambiguity proportional to the Polyakov loops along the boundaries, which can be reproduced by the overlap formalism. We show that the requirement on…
The triple phase transitions or simultaneous transitions of three different phases, namely topological, parity-time (PT) symmetry breaking, and metal-insulator transitions, are observed in an extension of PT symmetric non-Hermitian…
We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined…
Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in…
We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on…