Entanglement View of Dynamical Quantum Phase Transitions

Abstract

Non-analytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work .040602], we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript we extend and investigate the notion of p-and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.

Importance sampling scheme for the stochastic simulation of quantum spin dynamics

“…Such behavior points to an instability of the recursive solution in this region, which could be due to the coexistence of different minima yielding a comparable action; the leading and subleading contributions would then switch at a critical time t * SP ≈ 0.406. These observations suggest that DQPTs in |A dd | 2 are associated with an abrupt change of the product-state configuration carrying the largest contribution to the quantum dynamics, consistently with recent findings [44]. This immediately generalizes the phenomenology of ground-state QPTs in the disentanglement formalism, where QPTs are associated with an abrupt change of the dominant trajectory as a function of a control parameter [31].…”

“…The full quantum dynamics, obtained from sampling, includes the additional effects of entanglement on top of the optimal SP product-state dynamics. This potentially explains the small difference between t * SP and the DQPT critical time t * : the product-state approximation provided by the SP field can only determine the DQPT location approximately, as a degree of entanglement is always needed to fully capture these phenomena [44].…”

Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model

“…Extending this idea to the nonequilibrium realm, a DQPT at a critical time t * (instead of a critical control parameter) is said to occur when during the dynamics, such zeros are crossed [15]. A vast amount of recent theoretical research has been devoted to study this beautiful insight in systems of different nature, namely spin [15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], fermionic [33][34][35][36][37], bosonic [38][39][40][41][42][43], and hybrid models [44]. This effort also includes the analysis of the impact of ingredients such as disorder [45,46] and topological order [47,48].…”

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

“…In traditional quantum information approaches, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement [42][43][44], quantum Fisher information [45,46], fidelity [47][48][49] and so on. These quantities are sensitive to the quantum criticality, and often serve as a signature of transition points.…”