相关论文: Circuit Complexity across a Topological Phase Tran…
Non-Hermiticity enriches the contents of topological classification of matter including exceptional points, bulk-edge correspondence and skin effect. Gain and loss can be described by imaginary diagonal elements in Hamiltonians and the…
The inclusion of long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. By means of the scattering approach, we prove that the Majorana states \textit{soften},…
We develop a theory of the non-local transport of two counter-propagating $\nu = 1$ quantum Hall edges coupled via a narrow disordered superconductor. The system is self-tuned to the critical point between trivial and topological phases by…
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…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
A current flowing through a one-dimensional Kitaev chain induces a spatial modulation in its superconducting pairing, characterized by a wave vector $Q$, which is known to induce two types of topological phase transitions: one is the…
We link the presence of "unnecessary" quantum critical surfaces within a single gapped phase of matter to the non-trivial topology of families of gapped Hamiltonians that encircle the critical surface. We study a specific set of…
Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a…
We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and $\alpha$-RuCl$_3$. In the recent experiment of $\alpha$-RuCl$_3$, the signature of a nematic transition…
Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and…
We have applied the real space quantum renormalization group approach to study the topological quantum phase transition in the one-dimensional chain of a spinless p-wave superconductor. We investigate the behavior of local compressibility…
We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two…
Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological…
We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…
In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for…