scholarly journals Random transverse-field Ising chain with long-range interactions

2014 ◽  
Vol 107 (4) ◽  
pp. 47008 ◽  
Author(s):  
R. Juhász ◽  
I. A. Kovács ◽  
F. Iglói
Keyword(s):  
Long Range ◽  
Transverse Field ◽  
Ising Chain ◽  
Long Range Interactions

scholarly journals Coexistence of coarsening and mean field relaxation in the long-range Ising chain

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Federico Corberi ◽  
Alessandro Iannone ◽  
Manoj Kumar ◽  
Eugenio Lippiello ◽  
Paolo Politi
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Characteristic Time ◽  
Opposite Sign ◽  
Mean Field ◽  
Ising Chain ◽  
One Dimensional ◽  
Dynamical Scaling ◽  
Long Range Interactions ◽  
The One

We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance rr decaying as r^{-\alpha}r−α. For \alpha =0α=0, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with \alpha >1α>1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0<\alpha <10<α<1, we show that the system shows both features, with probability P_\alpha (N)Pα(N) of having the latter one, with the different limiting behaviours \lim _{N\to \infty}P_\alpha (N)=0limN→∞Pα(N)=0 (at fixed \alpha<1α<1) and \lim _{\alpha \to 1}P_\alpha (N)=1limα→1Pα(N)=1 (at fixed finite NN). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time \tau _\alpha (N)\sim N^\alphaτα(N)∼Nα.

scholarly journals Higher-order and fractional discrete time crystals in clean long-range interacting systems

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Andrea Pizzi ◽  
Johannes Knolle ◽  
Andreas Nunnenkamp
Keyword(s):  
Long Range ◽  
Discrete Time ◽  
Transverse Field ◽  
Higher Order ◽  
Periodically Driven ◽  
Semiclassical Methods ◽  
Long Range Interactions ◽  
Interacting Systems ◽  
Equilibrium Phases ◽  
Time Crystals

AbstractDiscrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different ‘higher-order’ discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

scholarly journals Dynamical phase diagram of a quantum Ising chain with long-range interactions

2019 ◽  
Vol 100 (18) ◽  
Author(s):  
Giulia Piccitto ◽  
Bojan Žunkovič ◽  
Alessandro Silva
Keyword(s):  
Phase Diagram ◽  
Long Range ◽  
Ising Chain ◽  
Dynamical Phase ◽  
Long Range Interactions
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