Related papers: Geometric phases and competing orders in two dimen…
Macroscopic properties of multiferroics, the systems that show simultaneously two types of ordering, could be controlled by the external fields of different nature. We analyze the behavior of multiferroics with antiferro-(AFM) and…
These are lectures presented at the summer course on ``Low Dimensional Quantum Field Theories for Condensed Matter Physicists'', 24 Aug. to 4 Sep. 1992, Trieste, Italy. I review recent work, performed in collaboration primarily with N. Read…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…
The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements…
The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to…
Quantum Electrodynamics in 2+1 dimensions (QED$_3$) with two Dirac fermions displays time reversal symmetry, nontrivial SPT phases and anomalies. The fate of this theory in its strongly coupled regime has been debated extensively.…
We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this…
We study the influence of the antiferromagnetic order on the surface states of topological insulators. We derive an effective Hamiltonian for these states, taking into account the spatial structure of the antiferromagnetic order. We obtain…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space…
This paper continues the author's work \cite{PartI}, where a new framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation discovered. Here, the nonlinear Dirac equation is solved and…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
We perform a detailed analysis of high-order harmonic generation in diatomic molecules within the strong-field approximation, with emphasis on quantum-interference effects. Specifically, we investigate how the different types of electron…
We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the…
The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behaviour of the geometric phase during a linear quench caused by a gradual turning off of…
We perform a Hartree-Fock calculation in order to describe the ground state of a vertical double quantum dot in the absence of magnetic fields parallel to the growth direction. Intra- and interdot exchange interactions determine the singlet…
We apply quantum field theory to study the excitation spectrum of doped two-leg ladders. It follows from our analysis that throughout most of the phase diagram the spectrum consists of degenerate quartets of kinks and anti-kinks and a…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
We describe four phases found in two-dimensional quantum antiferromagnets. Two of them display long range order at T=0: the N\'eel state and the Valence Bond Crystal. The last two are Spin-Liquids. Properties of these different states are…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…