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We study the generation and propagation of local perturbations in a quantum many-body spin system. In particular, we study the Ising model in transverse field in the presence of a local field defect at one edge. This system possesses a rich…
Open driven quantum systems have defined a powerful paradigm of nonequilibrium phases and phase transitions; however, quantum phase transitions are generically not expected in this setting due to the decohering effect of dissipation. In…
We study dynamics of the one-dimensional Ising model in the presence of static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find that the correlations decay as a power law. We uncover a…
We investigate analytically and numerically an Ising spin model with ferromagnetic coupling defined on random graphs corresponding to Feynman diagrams of a $\phi^q$ field theory, which exhibits a mean field phase transition. We explicitly…
We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization…
A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we…
The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In…
The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte…
We study the quantum Ising model in D dimensions with the equation of motion technique, in combination with the Majorana representation for spins. The decoupling scheme used for the Green's functions is based on the hierarchy of…
For the quantum phase transition in the transverse-field Ising chain, Kramers-Wannier duality not only protects its critical properties but also pinpoints the location of the phase transition. Its role in out-of-equilibrium, monitored…
We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions $\sigma_i^z\sigma_{i+1}^z$ and $\sigma_i^x\sigma_{i+1}^x$, alternating between even/odd…
We use Monte Carlo simulations to study a dynamically triangulated disk with Ising spins on the vertices and a boundary magnetic field. For the case of zero magnetic field we show that the model possesses three phases. For one of these the…
The phase transitions in the transverse field Ising model in a competing spatially modulated (periodic and oscillatory) longitudinal field are studied numerically. There is a multiphase point in absence of the transverse field where the…
We study the robustness of the Floquet quantum Ising model against integrability-breaking perturbations, focusing on the phase hosting both Majorana zero and $\pi$ modes. A recent work [Phys. Rev. B 110, 075117, (2024)] observed that the…
The topological degeneracy is a characteristic of quantum phase diagram in an Ising chain with transverse field. We revisit the phase diagram at nonzero temperature of an Ising chain with two types of open boundary conditions. In this work,…
We study the quantum phase transition in a spin chain with variable Ising interaction and position-dependent coupling to a resonator field. Such a complicated model, usually not present in natural physical systems, can be simulated by an…
The thesis contains theoretical study of number of systems in low dimension, which are related to quantum Ising model. The main results are emergence of Majorana fermions in condensed matter system. We discuss an array of cavity-QED system,…
We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and…