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Register a new userDiagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
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We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which can not show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.
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We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions can still occur for quenches within a single topological phase. We also investigate the boundary contributions from the presence of the topologically protected edge states of this model. Plateaus in the boundary return rate are related to the topology of the time evolving Hamiltonian, and hence to a dynamical bulk-boundary correspondence. We go on to consider the dynamics of the entanglement entropy generated after a quench, and its potential relation to the critical times of the dynamical quantum phase transitions. Finally, we investigate the fidelity susceptibility as an indicator of the topological phase transitions, and find a simple scaling law as a function of the number of bands of our multiband model which is found to be the same for both bulk and boundary fidelity susceptibilities.
We study the Kitaev-Ising model, where ferromagnetic Ising interactions are added to the Kitaev model on a lattice. This model has two phases which are characterized by topological and ferromagnetic order. Transitions between these two kinds of order are then studied on a quasi-one dimensional system, a ladder, and on a two dimensional periodic lattice, a torus. By exactly mapping the quasi-one dimensional case to an anisotropic XY chain we show that the transition occurs at zero $lambda$ where $lambda$ is the strength of the ferromagnetic coupling. In the two dimensional case the model is mapped to a 2D Ising model in transverse field, where it shows a transition at finite value of $lambda$. A mean field treatment reveals the qualitative character of the transition and an approximate value for the transition point. Furthermore with perturbative calculation, we show that expectation value of Wilson loops behave as expected in the topological and ferromagnetic phases.
The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of different symmetries, has become a large widely studied field in its own right. Additionally an analogy between phase transitions, described by non-analyticities in the derivatives of the free energy, and non-analyticities which occur in dynamically evolving correlation functions has been drawn. These are called dynamical phase transitions and one is often now far from the equilibrium situation. In these short lecture notes we will give a brief overview of the history of these concepts, focusing in particular on the way in which dynamical phase transitions themselves can be used to shed light on topological phase transitions and topological phases. We will go on to focus, first, on the effect which the topologically protected edge states, which are one of the interesting consequences of topological phases, have on dynamical phase transitions. Second we will consider what happens in the experimentally relevant situations where the system begins either in a thermal state rather than the ground state, or exchanges particles with an external environment.
We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n sim 1/sqrt{tau} where 1/tau is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent non-zero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d dimensional quantum model, where the quench takes the system through a d-m dimensional gapless (critical) surface characterized by correlation length exponent u and dynamical critical exponent z, the defect density n sim 1/tau^{m u /(z u +1)}. We also discuss the variation of the shape and the spatial extent of the defect correlation function with the change of both the rate of quench and the model parameters and compute the entropy generated during such a quench process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.
Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the systems quantum critical point. We show that the systems temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in adiabatic processes. We take the one-dimensional transverse-field Ising model and spinless fermion system as concrete examples to show that the inverse temperature might become divergent around their critical points. Since the temperature is a measurable quantity in experiments, our work, therefore, provides a practicable proposal to detect quantum phase transitions.
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