Search results for "Degeneracy"

Frustration, Entanglement, and Correlations in Quantum Many Body Systems

2013

We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.

Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization

2014

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation…

Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy

2004

We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabat…

Scattering of Particles by Potentials

2013

The three prototypes of spectra of self-adjoint operators, the discrete spectrum, with or without degeneracy, the continuous spectrum, and the mixed spectrum, as well as the corresponding wave functions, contain important information about the physical systems that they describe

Lévy distributions and disorder in excitonic spectra.

2020

We study analytically the spectrum of excitons in disordered semiconductors like transition metal dichalcogenides, which are important for photovoltaic and spintronic applications. We show that ambient disorder exerts a strong influence on the exciton spectra. For example, in such a case, the wellknown degeneracy of the hydrogenic problem (related to Runge–Lenz vector conservation) is lifted so that the exciton energy starts to depend on both the principal quantum number n and orbital l. We model the disorder phenomenologically substituting the ordinary Laplacian in the corresponding Schro¨dinger equation by the fractional one with Le´vy index m, characterizing the degree of disorder. Our v…

Thermodynamics of supercooled liquids in the inherent structure formalism: a case study

2000

In this article we review the thermodynamics of liquids in the framework of the inherent structure formalism. We then present calculations of the distribution of the basins in the potential energy of a binary Lennard-Jones mixture as a function of temperature. The comparison between the numerical data and the theoretical formalism allows us to evaluate the degeneracy of the inherent structures in a bulk system and to estimate the energy of the lowest energy disordered state (the Kauzmann energy). We find that, around the mode-coupling temperature, the partition function of the liquid is approximated well by the product of two loosely coupled partition functions, one depending on the inheren…

Quantum order by disorder in the Kitaev model on a triangular lattice

2015

We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-n…

Extraction of cluster parameters with future Sunyaev-Zel'dovich observations

2003

The Sunyaev-Zel'dovich (SZ) effect of galaxy clusters is characterized by three parameters: Compton parameter, electron temperature and cluster peculiar velocity. In the present study we consider the problem of extracting these parameters using multi-frequency SZ observations only. We show that there exists a parameter degeneracy which can be broken with an appropriate choice of frequencies. As a result we discuss the optimal choice of observing frequencies from a theoretical point of view. Finally, we analyze the systematic errors (of the order micro K) on the SZ measurement introduced by finite bandwidths, and suggest a possible method of reducing these errors.

Topological field theory

1991

Confusing nonzero theta(13) with nonstandard interactions in the solar neutrino sector

2009

Solar and KamLAND data are in slight tension when interpreted in the standard two-flavor oscillations framework and this may be alleviated allowing for a non-zero value of the mixing angle theta_13. Here we show that, likewise, non-standard flavor-changing interactions (FCI), possibly intervening in the propagation of solar neutrinos, are equally able to alleviate this tension and therefore constitute a potential source of confusion in the determination of theta_13. By performing a full three-flavor analysis of solar and KamLAND data in presence of FCI we provide a quantitative description of the degeneracy existing between theta_13 and the vectorial coupling eps_e\tau^dV characterizing the…