Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points

Abstract

We address the out-of-equilibrium dynamics of many-body systems subject to slow time-dependent round-trip protocols across quantum and classical (thermal) phase transitions. We consider protocols where one relevant parameter w is slowly changed across its critical point wc = 0, linearly in time with a large time scale ts, from wi < 0 to wf > 0 and then back to wi < 0, thus entailing multiple passages through the critical point. Analogously to the one-way Kibble-Zurek protocols across a critical point, round-trip protocols develop dynamic scaling behaviors at both classical and quantum transitions, put forward within renormalization-group frameworks. The scaling scenario is analyzed within some paradigmatic models undergoing quantum and classical transitions belonging to the two-dimensional Ising universality class, such as one-dimensional quantum Ising models and fermionic wires, and two-dimensional classical Ising models (supplemented with a purely relaxational dynamics). While the dynamic scaling frameworks are similar for classical and quantum systems, substantial differences emerge due to the different nature of their dynamics, which is purely relaxational for classical systems (implying thermalization in the large-time limit at fixed model parameters), and unitary in the case of quantum systems. In particular, when the critical point separates two gapped (short-ranged) phases and the extreme value wf > 0 is kept fixed in the large-ts limit of the round-trip protocol, we observe hysteresis-like scenarios in classical systems, while quantum systems do not apparently develop a sufficiently robust scaling limit along the return way, due to the presence of rapidly oscillating relative phases among the relevant quantum states.

24 pages, Phys. Rev. B in press

References in corpus (22)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Universal adiabatic dynamics across a quantum critical point
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Emergence of coherence and the dynamics of quantum phase transitions
• Phase transitions in the early and the present Universe
• Vortex quantum creation and winding number scaling in a quenched spinor Bose gas
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Finite-size scaling at first-order quantum transitions
• Reverse quantum annealing of the $p$-spin model with relaxation
• Robustness of adiabatic passage trough a quantum phase transition
• Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions
• Finite-size scaling at the first-order quantum transitions of quantum Potts chains
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Scaling of decoherence and energy flow in interacting quantum spin systems
• Dynamic finite-size scaling at first-order transitions

Cited by in corpus (2)

• Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations
• Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system