Adiabatic quantum dynamics of a random Ising chain across its quantum critical point

Abstract

We present here our study of the adiabatic quantum dynamics of a random Ising chain across its quantum critical point. The model investigated is an Ising chain in a transverse field with disorder present both in the exchange coupling and in the transverse field. The transverse field term is proportional to a function $\Gamma (t)$ which, as in the Kibble-Zurek mechanism, is linearly reduced to zero in time with a rate ${\tau }^{-1}$, $\Gamma (t)=-t/\tau$, starting at $t=-\infty$ from the quantum disordered phase ($\Gamma =\infty$) and ending at $t=0$ in the classical ferromagnetic phase ($\Gamma =0$). We first analyze the distribution of the gaps -- occurring at the critical point ${\Gamma }_c=1$ -- which are relevant for breaking the adiabaticity of the dynamics. We then present extensive numerical simulations for the residual energy $E_{\mathrm{res}}$ and density of defects ${\rho }_k$ at the end of the annealing, as a function of the annealing inverse rate $\tau$. %for different lenghts of the chain. Both the average $E_{\mathrm{res}}(\tau )$ and ${\rho }_k(\tau )$ are found to behave logarithmically for large $\tau$, but with different exponents, $[E_{\mathrm{res}}(\tau )/L{]}_{\mathrm{av}}\sim 1/{\ln }^{\zeta }(\tau )$ with $\zeta \approx 3.4$, and $[{\rho }_k(\tau ){]}_{\mathrm{av}}\sim 1/{\ln }^2(\tau )$. We propose a mechanism for $1/{\ln }^2\tau$-behavior of $[{\rho }_k{]}_{\mathrm{av}}$ based on the Landau-Zener tunneling theory and on a Fisher's type real-space renormalization group analysis of the relevant gaps. The model proposed shows therefore a paradigmatic example of how an adiabatic quantum computation can become very slow when disorder is at play, even in absence of any source of frustration.

10 pages, 11 figures; v2: added references, published version

References in corpus (33)

• Efficient classical simulation of slightly entangled quantum computations
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Theory of Quantum Annealing of an Ising Spin Glass
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Quantum Search by Local Adiabatic Evolution
• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• 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
• Entanglement entropy of random quantum critical points in one dimension
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Quantum annealing of the Traveling Salesman Problem
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Entropy and Correlation Functions of a Driven Quantum Spin Chain
• Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
• Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
• Dynamics of a quantum phase transition in the random Ising model
• Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains
• Residual Energies after Slow Quantum Annealing
• Optimization by Quantum Annealing: Lessons from Simple Cases
• Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
• Adiabatic quantum computation and quantum phase transitions
• Robustness of adiabatic passage trough a quantum phase transition
• Convergence theorems for quantum annealing
• Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions
• Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain
• Monte Carlo studies of quantum and classical annealing on a double-well

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