Browsing by Subject "Quantum phase transitions"

Now showing 1 - 6 of 6

Open Access
Generalized Aubry-Andre-Harper model with modulated hopping and p-wave pairing
(American Physical Society, 2019) Yahyavi, Mohammad; Hetenyi, Balazs; Tanatar, Bilal
We study an extended Aubry-André-Harper model with simultaneous modulation of hopping on-site potential and p-wave superconducting pairing. For the case of commensurate modulation of β=1/2 it is shown that the model hosts four different types of topological states: Adiabatic cycles can be defined which pump particles two types of Majorana fermions or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multifractal analysis. In addition we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual rather than sharp. When in addition the on-site potential modulation is incommensurate we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangularlike near zero pairing when gap closure occurs they are squarelike and hexagonal-like for larger pairing but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.
Open Access
Local entanglement and string order parameter in dimerized models
(IOP, 2019-09) Bahovadinov, Murod S; Gülseren, Oğuz; Schnack, J.
In this letter, we propose an application of string order parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain. As a generalized form of dimerized model, we consider a one-dimensional spin-1/2 XX model with alternating spin couplings. We employ Jordan–Wigner fermionization to map this model to the spinless Su–Schrieffer– Heeger fermionic model (SSH) with generalized hopping signs. We demonstrate a phase transition between a trivial insulating phase and the Haldane phase by the exact analytical evaluation of reconstructed SOPs which are represented as determinants of Toeplitz matrices with the given generating functions. To get more insight into the topological quantum phase transition (tQPT) and microscopic correlations, we study the pairwise concurrence as a local entanglement measure of the model. We show that the first derivative of the concurrence has a non-analytic behaviour in the vicinity of the tQPT, like in the second order trivial QPTs.
Open Access
Metal-insulator transitions in bilayer electron-hole systems in transition metal dichalcogenides
(American Physical Society, 2021-11-29) Chui, S. T.; Wang, N.; Tanatar, Bilal
We investigated metal-insulator transitions for double-layer two-dimensional electron-hole systems in transition metal dichalcogenides stacked on opposite sides of thin layers of boron nitride. The interparticle interaction is calculated by including the screening due to the polarization charges at different interfaces, including that at the encapsulation and at the substrate of experimental structures. We compute and compare the energies of the metallic electron-hole plasma and the proposed insulating exciton solid with fixed-node diffusion Monte Carlo simulation including the high valley degeneracy of the electron bands. We found that for some examples of current experimental structures, the transition electron/hole density is in an experimentally accessible range between 4.1×10 12cm−2 and 14.5×10 12cm−2 for spacer thicknesses between 2.5 and 7.5 nm. Our result raises the possibility of exploiting this effect for logic device applications.
Open Access
Quantum phase transitions from analysis of the polarization amplitude
(American Physical Society, 2019) Hetenyi, Balazs; Dora, B.
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a discretized characteristic function and derive formulas for its cumulants and moments. In the case of a noninteracting system, our scheme leads to the gauge-invariant cumulants known from polarization theory. We study the behavior of such cumulants for several interacting models. In a one-dimensional system of spinless fermions with nearest neighbor interaction the transition at which gap closure occurs can be clearly identified from the finite size scaling exponent of the variance. When next nearest neighbor interactions are turned on a model with a richer phase diagram emerges, but the finite size scaling exponent is still an effective way to identify the localization transition.
Open Access
Scaling and renormalization in the modern theory of polarization: application to disordered systems
(American Physical Society, 2021-12-15) Hetényi, Balázs; Parlak, Selçuk; Yahyavi, Mohammad
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension, the renormalized disorder strength tends to infinity, indicating the entire absence of extended states. Zero (infinite) disorder is a repulsive (attractive) fixed point. In two and three dimensions, at small system sizes, two additional fixed points appear, both at finite disorder: Wa(Wr) is attractive (repulsive) such that Wa
Open Access
Topological aspects of charge transport in quantum many-body systems
(2019-01) Yahyavi, Mohammad
Motivated by the recent proposals and developments of topological insulators and topological superconductors for their potential applications in electronic devices and quantum computing, we have theoretically studied topological properties of quantum many-body systems. First, we calculate the gauge-invariant cumulants (and moments) associated with the Zak phase. The first cumulant corresponds to the Berry phase itself, the others turn out to be the associated spread, skew, kurtosis, etc. The cumulants are shown to be gauge invariant. We reconstruct the underlying probability distribution of the polarization by maximizing the information entropy and applying the moments as constraints in the Rice-Mele model and in the interacting, spinless Su-Schrieffer-Heeger model. When the Wannier functions are localized within one-unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We follow the probability distribution of the polarization in cycles around the topologically nontrivial point of these models. Secondly, we have constructed a topological one-dimensional analog of the Haldane and Kane-Mele models in two dimensions, with hexagonal lattices. Our Haldane one-dimensional analog model belongs to the C and CI symmetry classes, depending on the parameters, but, due to re ection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We also construct a topological one-dimensional ladder model following the steps which lead to the Kane-Mele model in two dimensions. We couple two Haldane-type ladder models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of re ection symmetries. Thirdly, we consider the edge at the interface of a simple tight-binding model and a band insulator. We find that crossings in the band structure (one dimensional Dirac points) appear when an interface is present in the system. We calculate the hopping energy resolved along lines of bonds parallel to the interface as a function of distance from the interface. Similarly, we introduce a transport coe cient (Drude weight) for charge currents running parallel to the interface. We find that charge mobility (both the kinetic energy and the Drude weight) is significantly enhanced in the surface of the tight-binding part of the model near the interface. Finally, we study a variant of the generalized Aubry-Andre-Harper model with the effect of introducing next nearest-neighbor p-wave superconducting pairing with incommensurate and commensurate cosine modulations. We extend generalized Aubry-Andr e-Harper model with p-wave superconducting to topologically equivalent and nontrivial "anancestor" two-dimensional p-wave superconducting model. It is found that in incommensurate (commensurate) modulation, by varying next nearest-neighbor p-wave pairing order parameter, the system can switch between extended states and localized states (fully gapped phase and a gapless phase).