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Register a new userLarge geometric phases and non-elementary monopoles
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Degeneracies in the spectrum of an adiabatically transported quantum system are important to determine the geometrical phase factor, and may be interpreted as magnetic monopoles. We investigate the mechanism by which constraints acting on the system, related to local symmetries, can create arbitrarily large monopole charges. These charges are associated with different geometries of the degeneracy. An explicit method to compute the charge as well as several illustrative examples are given.
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The monopole for the geometric curvature is studied for non-Hermitian systems. We find that the monopole contains not only the exceptional points but also branch cuts. As the mathematical choice of branch cut in the complex plane is rather arbitrary, the monopole changes with the branch-cut choice. Despite this branch-cut dependence, our monopole is invariant under the $GL(l,mathbb{C})$ gauge transformation that is inherent in non-Hermitian systems. Although our results are generic, they are presented in the context of a two-mode non-Hermitian Dirac model. A corresponding two-mode Hermitian system is also discussed to illustrate the essential difference between monopoles in Hermitian systems and non-Hermitian systems.
Although stoquastic Hamiltonians are known to be simulable via sign-problem-free quantum Monte Carlo (QMC) techniques, the non-stoquasticity of a Hamiltonian does not necessarily imply the existence of a QMC sign problem. We give a sufficient and necessary condition for the QMC-simulability of Hamiltonians in a fixed basis in terms of geometric phases associated with the chordless cycles of the weighted graphs whose adjacency matrices are the Hamiltonians. We use our findings to provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models. We also demonstrate why the simulation of truly sign-problematic models using the QMC weights of the stoquasticized Hamiltonian is generally sub-optimal. We offer a superior alternative.
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.
In this reply, we address the comment by Ericsson and Sjoqvist on our paper [Phys. Rev. A {bf 84}, 034103 (2011)]. We point out that the zero gauge field is not the evidence of trivial geometric phase for a non-Abelian SU(2) gauge field. Furthermore, the recalculation shows that the non-Abelian geometric phase we proposed in the three-level $Lambda$ system is indeed experimentally detectable.
We show that the definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naive direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting artifacts can induce a false inversion of population or a false adiabaticity. We show that the inconsistency can be avoided by introducing geometric phases in another possible definition of populations. An example is given which demonstrates both the anomalous effects and their removal by our approach.
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