FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS

1992 ◽  
Vol 06 (14) ◽  
pp. 2439-2469 ◽  
Author(s):  
P. SEN ◽  
B. K. CHAKRABARTI
Keyword(s):  
Excited States ◽  
Transverse Field ◽  
Ising Models ◽  
Quantum Systems ◽  
Nearest Neighbour ◽  
Competing Interactions ◽  
Annni Model ◽  
Kirkpatrick Model ◽  
Transverse Fields ◽  
Exact Diagonalisation

The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.

A model for polysomatism

1986 ◽  
Vol 50 (355) ◽  
pp. 149-156 ◽  
Author(s):  
Geoffrey D. Price ◽  
Julia Yeomans
Keyword(s):  
Magnetic Field ◽  
Chemical Potential ◽  
Spin Model ◽  
Nearest Neighbour ◽  
Key Factors ◽  
Competing Interactions ◽  
Annni Model ◽  
The Stability

AbstractWe show that the structures and phases developed in a variety of polysomatic series, including the biopyroboles, are similar to those predicted by a simple spin model—the Axial Next-Nearest-Neighbour Ising (ANNNI) model in a magnetic field. We argue that the different polysomatic structures can be considered as thermodynamically stable phases, composed of ordered sequences of chemically distinct structural modules. We suggest that the key factors which determine the stability of polysomatic phases are (a) the chemical potential, which controls the proportion of the different structural modules, and (b) the competing interactions between first and second neighbour modules within the structures.

scholarly journals USE OF THE WHIRLIGIG PRINCIPLE FOR STABILIZING THE INITIAL STATES OF SOME CLASSIC AND QUANTUM SYSTEMS

2020 ◽  
pp. 78-81
Author(s):  
V.A. Buts
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Quantum Systems ◽  
Nuclear Systems ◽  
Initial States

It is shown that the whirligig principle can be used for stabilization of the initial states of some classical and quantum systems. This feature of the whirligig principle is demonstrated by simple examples. The most important result of this work is the proof of the fact that the stabilization of the excited states of quantum systems can be realized by acting not on the quantum system itself, but by acting on the states into which the system must go. Potentially, this result can be used to stabilize excited nuclear systems.

scholarly journals Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Silvia Pappalardi ◽  
Anatoli Polkovnikov ◽  
Alessandro Silva
Keyword(s):  
Quantum Physics ◽  
Transverse Field ◽  
Many Body ◽  
Initial State ◽  
Large N ◽  
Semiclassical Dynamics ◽  
Long Time ◽  
Kirkpatrick Model ◽  
Ehrenfest Time ◽  
Many Body Systems

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

scholarly journals Modelling equilibration of local many-body quantum systems by random graph ensembles

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 273 ◽  
Author(s):  
Daniel Nickelsen ◽  
Michael Kastner
Keyword(s):  
Hilbert Space ◽  
Random Matrices ◽  
Network Theory ◽  
Maximum Flow ◽  
Quantum Systems ◽  
Complex Matrix ◽  
Many Body ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Exact Diagonalisation

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner's full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.

The origins of the colours of natural yellow, blue, and green sapphires

1972 ◽  
Vol 25 (7) ◽  
pp. 1371 ◽  
Author(s):  
J Ferguson ◽  
PE Fielding
Keyword(s):  
Temperature Dependence ◽  
Absorption Spectra ◽  
Excited States ◽  
Exchange Parameter ◽  
Nearest Neighbour ◽  
Electronic Excitations ◽  
Heisenberg Exchange ◽  
Synthetic Crystals

An analysis of the absorption spectra of natural yellow sapphires shows that the absorption is due to single Fe3+ ions and pairs of ions Fe3+-O2--Fe3+. Assignments of all levels from the 4G, 4P, and 4D have been made as well as four simultaneous electronic excitations of a pair of ions. The temperature dependence of the intensity of the pair absorption shows that one pair is mainly involved, probably the fourth- nearest neighbour pair. The value of the Heisenberg exchange parameter (J Sa. Sb) lies in the range 30-40 K. Estimates of this parameter for various excited states have been made. Synthetic yellow sapphires have spectra which duplicate the natural specimens. Blue and green natural sapphires have, in addition to the bands present in the spectra of yellow sapphires, spectra with bands at 17800 (┴C), 14200 (//c), 11500 (┴C), and 10000 om-1 (//c). The first two can be linked to Fe,Ti pairs and the evidence favours the nearest neighbour pair Ti4+-O2?Fe2+ for the 17800 cm-1 band and possibly the first neighbour pair for the 14200 cm-1 band. The second two can be produced in synthetic crystals by growth from fluoride-containing flux and the evidence supports an explanation involving second-nearest neighbour pairs Fe2+- O2--Fe3+ for the 11500 cm-1 absorption and first neighbours for the 10000 om-1 absorption.

Transverse Field in the Sherrington-Kirkpatrick Model

1987 ◽  
Vol 26 (S3-3) ◽  
pp. 2107
Author(s):  
Tetsuya Yamamoto ◽  
Hiroumi Ishii
Keyword(s):  
Transverse Field ◽  
Kirkpatrick Model
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