Cairo lattice with time-reversal non-invariant vertex couplings
- URL: http://arxiv.org/abs/2312.13827v1
- Date: Thu, 21 Dec 2023 13:18:07 GMT
- Title: Cairo lattice with time-reversal non-invariant vertex couplings
- Authors: Marzieh Baradaran and Pavel Exner
- Abstract summary: We analyze the spectrum of a periodic quantum graph of the Cairo lattice form.
We discuss two modifications of the model in which this is not the case.
While different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We analyze the spectrum of a periodic quantum graph of the Cairo lattice
form. The used vertex coupling violates the time reversal invariance and its
high-energy behavior depends on the vertex degree parity; in the considered
example both odd and even parities are involved. The presence of the former
implies that the spectrum is dominated by gaps. In addition, we discuss two
modifications of the model in which this is not the case, the zero limit of the
length parameter in the coupling, and the sign switch of the coupling matrix at
the vertices of degree three; while different they both yield the same
probability that a randomly chosen positive energy lies in the spectrum.
Related papers
- Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
We introduce a class of quantum optical Hamiltonian characterized by three-body couplings.
We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
arXiv Detail & Related papers (2022-04-07T15:39:21Z) - Magnetic ring chains with vertex coupling of a preferred orientation [0.0]
We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links.
The magnetic field influences the probability that an energy belongs to the spectrum in the tight-chain case, and also it can turn some spectral bands into infinitely eigenvalues.
arXiv Detail & Related papers (2022-01-05T09:02:10Z) - Quantum correlations, entanglement spectrum and coherence of
two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
We study the ground state properties of the one-dimensional extended Hubbard model at half-filling.
In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
arXiv Detail & Related papers (2021-10-29T21:02:24Z) - Probing many-body systems near spectral degeneracies [0.0]
diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times.
This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking.
Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction.
arXiv Detail & Related papers (2021-08-30T12:02:33Z) - Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings.
We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z) - Kagome network with vertex coupling of a preferred orientation [0.0]
We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice.
The kagome lattice example shows that even in graphs with such an uncommon universality coupling spectral may hold.
arXiv Detail & Related papers (2021-06-30T12:35:12Z) - Spectral clustering under degree heterogeneity: a case for the random
walk Laplacian [83.79286663107845]
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree.
In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
arXiv Detail & Related papers (2021-05-03T16:36:27Z) - Multiple ground-state instabilities in the anisotropic quantum Rabi
model [0.0]
We study the anisotropic variant of the quantum Rabi model with different coupling strengths of the rotating and counter-rotating wave terms.
The anisotropy preserves the parity symmetry of the original model.
We find analytically that the ground-state and the first excited state can cross several times.
arXiv Detail & Related papers (2021-01-29T04:21:08Z) - Spectrum of periodic chain graphs with time-reversal non-invariant
vertex coupling [0.0]
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair.
We discuss the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero.
arXiv Detail & Related papers (2020-12-28T16:35:45Z) - Equivalence of approaches to relational quantum dynamics in relativistic
settings [68.8204255655161]
We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector.
We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
arXiv Detail & Related papers (2020-07-01T16:12:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.