Related papers: Geometric Phase and Quantum Phase Transition : Two…
The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus…
We study the coupled-top model with three large spins located on a triangle. Depending on the coupling strength, there exist three phases: disordered paramagnetic phase, ferromagnetic phase, and frustrated antiferromagnetic phase, which can…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by…
We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the $(t,t')$ Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…
In the framework of open quantum systems, we study the geometric phase acquired by freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We find that,…
We present a new approach to quantum computation involving the geometric phase. In this approach, an entire computation is performed by adiabatically evolving a suitably chosen quantum system in a closed circuit in parameter space. The…
For a finite XY chain and a finite two-dimensional Ising lattice, it is shown that the paramagnetic ground state is adiabatically transformed to the GHZ state in the ferromagnetic phase by slowly turning on the magnetic field. The fidelity…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
We have constructed a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable…
We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation,…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
In this paper, we investigate the geometric phase of the field interacting with $\Xi $-type moving three-level atom. The results show that the atomic motion and the field-mode structure play important roles in the evolution of the system…
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions…