On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

Abstract

We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensor-network ansatz. We discuss how more reliable results could be obtained.

Steady-state susceptibility in continuous phase transitions of dissipative systems

“…However, as the coupling strength varying, the steady states of the system may undergo a phase transition to the ordered phase with nonzero magnetization on the xy plane which is referred to as the ferromagnetic phase implying the spontaneous broken the Z 2 symmetry. The steady-state phase transitions in dissipative spin-1/2 XYZ model has been widely studied by many literatures [8,9,14,15,26,28].…”

“…Due to the nonunitary nature of the dynamics and exponential growth of the dimension of Hilbert space of the system, it is challenge in the theoretic description and numerical simulation for the open quantum many-body systems. In recent years, a plenty of meaningful results have been obtained [8][9][10][11][12][13][14] and several numerical methods have been developed [15][16][17][18][19][20][21][22][23][24] in recent years. By combining the corner-space renormalization method [19] with the Monte Carlo wave-function trajectory method [25], Rota et.…”

Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

“…TN representations can be used to encode the many-body density matrix describing a mixed state and to study the dynamics of the Lindblad master equation, describing a system coupled to a Markovian bath [30][31][32][33][34][35][36][37]. A majority of the studies considered one-dimensional (1D) problems, for which matrix-product representations are particularly adapted, but some results could also be obtained for in other geometries [34,35,37,38].…”

Time-dependent variational principle for open quantum systems with artificial neural networks

“…Semi-classical [42][43][44][45] and mean-field like methods [46,47] provide a polynomial scaling in N but often suffer from uncontrolled approximations and numerical instabilities. Tensor network based approaches [1,2,[48][49][50][51][52][53][54][55][56] are limited to weakly entangled states and require further approximations if applied in dimensions d > 1 [57][58][59]. A recently introduced class of methods, that can potentially resolve many of these issues are Neural Network Quantum States (NQS) [60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”