Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

Abstract

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e., the exponent varies continuously with the parameter $\alpha$ that defines the path, up to a critical value $\alpha ={\alpha }_c$; on the other hand for $\alpha \ge {\alpha }_c$, the scaling exponent saturates to a constant value. We show that dynamically generated and {\it path($\alpha$)-dependent} effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a $d$-dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective {\it path-dependent} dimensional shift $d_0(\alpha )$ (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. Numerically obtained results are in good agreement with analytical predictions.

5 pages, 4 figures

References in corpus (35)

• Many-Body Physics with Ultracold Gases
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Universal adiabatic dynamics across a quantum critical point
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• 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''
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Transition times in the Landau-Zener model
• Entropy and Correlation Functions of a Driven Quantum Spin Chain
• Topology induced anomalous defect production by crossing a quantum critical point
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Optimal non-linear passage through a quantum critical point
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
• Quenching along a gapless line: A different exponent for defect density
• Defect production due to quenching through a multicritical point
• Theory of defect production in nonlinear quench across a quantum critical point
• Adiabatic quenches through an extended quantum critical region
• Adiabatic nonlinear probes of one-dimensional Bose gases
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
• Robustness of adiabatic passage trough a quantum phase transition
• Anomalous non-ergodic scaling in adiabatic multicritical quantum quenches
• Quenching through Dirac and semi-Dirac points in optical Lattices: Kibble-Zurek scaling for anisotropic Quantum-Critical systems
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

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• Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Quench dynamics and parity blocking in Majorana wires
• Oscillating fidelity susceptibility near a quantum multicritical point
• The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points
• Topological Blocking in Quantum Quench Dynamics
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment
• Dynamics of decoherence: universal scaling of the decoherence factor
• Suppressing defect production during passage through a quantum critical point
• Dynamical generation of Majorana edge correlations in a ramped Kitaev chain coupled to nonthermal dissipative channels
• Quenching Dynamics and Quantum Information
• Magnetic field dependence of the entanglement entropy of one dimensional spin systems in quantum phase transition induced by a quench
• Quantum Discord in a spin-1/2 transverse XY Chain Following a Quench
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Universal scaling in quenches across a discontinuity critical point
• Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model
• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Work statistics across a quantum critical surface
• Path dependent scaling of geometric phase near a quantum multi-critical point
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Kibble-Zurek mechanism from different angles: The transverse XY model and subleading scalings
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity
• Sudden quenches in quasiperiodic Ising model
• Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice
• Driven Critical Dynamics in Tricitical Point
• Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel