Critical behavior of dissipative two-dimensional spin lattices

Rota, Riccardo; Storme, F.; Bartolo, N.; Fazio, Rosario; Ciuti, Cristiano

doi:10.1103/physrevb.95.134431

Cited by 84 publications

(122 citation statements)

References 34 publications

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…The possibility to extrapolate the critical exponents for a dissipative quantum phase transition is very intriguing, since, to the best of our knowledge, the only numerical work in this context, that is present in the literature, is Ref. 39. However, since finite-size systems are considered there, it was only possible to estimate the finite-size ratio γ/ν, where ν denotes the critical exponent associated to the divergent behavior of the correlation length.…”

Section: Critical Behaviormentioning

confidence: 99%

“…Here we follow the approach of Rota et al 39 and discuss the magnetic linear response to an applied magnetic field in the x-y plane, which modifies the Hamiltonian in Eq. (8) according to:…”

Section: B Anisotropic Case and The Paramagnetic To Ferromagnetic Phmentioning

confidence: 99%

“…The phenomenology of this phase transition has recently received a lot of attention, and has been investigated at a Gutzwiller mean-field level 32 and by means of more sophisticated methods, including the cluster meanfield approach 53 , the corner-space renormalization technique 39 , and the projected entangled pair operators 58 . The phase transition point for the same choice of parameters of Eq.…”

Section: B Anisotropic Case and The Paramagnetic To Ferromagnetic Phmentioning

confidence: 99%

“…Here we see NLCE at work in an interacting twodimensional spin-1/2 model with incoherent spin relaxation 32 , which is believed to exhibit a rich phase diagram, and represents a testing ground for strongly correlated open quantum systems 39,53,58 . We will test our method both far from critical points, and in the proximity of a phase transition: in the first case NLCE allows us to accurately compute the value of the magnetization, while in the latter we are able to estimate the critical point as well as the critical exponent γ for the divergent susceptibility.…”

Section: Introductionmentioning

confidence: 99%

“…The phase-diagram of such lattice systems has been predicted to be incredibly rich [23][24][25][26][27][28][29][30] and can display spontaneous ordering associated with the breaking of a discrete [31][32][33] or continuous symmetry 34,35 possessed by the model. Recently, the critical behavior emerging at the onset of phase transitions started to be investigated by means of different analytical and numerical approaches [36][37][38][39] . Theoretically, while at equilibrium we have reached a fairly good understanding of several aspects of the manybody problem under the framework of textbook statistical mechanics, this is no longer the case for quantum systems coupled to some external bath.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Linked cluster expansions for open quantum systems on a lattice

et al. 2018

View full text Add to dashboard Cite

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

show abstract

Section: Critical Behaviormentioning

confidence: 99%

Section: B Anisotropic Case and The Paramagnetic To Ferromagnetic Phmentioning

confidence: 99%

Section: B Anisotropic Case and The Paramagnetic To Ferromagnetic Phmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linked cluster expansions for open quantum systems on a lattice

et al. 2018

View full text Add to dashboard Cite

show abstract

Estimation and Prediction of Typhoons and Wave Overtopping in Qingdao, China

Wang

Hao

et al. 2020

J. Ocean Univ. China

View full text Add to dashboard Cite

When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on octree to solve these difficulties. In our approach, scientific data is preprocessed before training, and a hierarchical octreebased data structure is built to guide sampling on the latent context grid. Each leaf node in the octree corresponds to an indivisible subblock of the volumetric data. The dimensions of the subblocks are different, making the number of sample points in each randomly cropped training data block to be adaptive. We reconstruct the octree at intervals according to loss distribution to perform the multi-stage training. With the Rayleigh-Bénard convection problem, we deploy our method to state-of-the-art models. We constructed adequate experiments to evaluate the training performance and model accuracy of our method. Experiments indicate that our sampling optimization improves the convergence performance of physics-constrained deep learning super-resolution solutions. Furthermore, the sample points and training time are significantly reduced with no drop in model accuracy. We also test our method in training tasks of other deep neural networks, and the results show our sampling optimization has extensive effectiveness and applicability. The code is publicly available at https://github.com/xinjiewang/octree-based sampling.

show abstract