We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between $d$ -dimensional quantum system with a $(d+1)$ -dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the $\pm J$ model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses. We have also breifly discussed the possibility of Quantum Annealing in context of kinetically constrained systems. Mean-field calculation for BCS superconductivity, Real-space RG calculation for one dimensional transverse Ising system, scattering amplitude calculation for tunneling through asymmetric barrier (useful for quantum kinetically constrained system) are given in the appendices.We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between $d$-dimensional quantum system with a $(d+1)$-dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the $\pm J$ model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses. We have also breifly discussed the possibility of Quantum Annealing in context of kinetically constrained systems. Mean-field calculation for BCS superconductivity, Real-space RG calculation for one dimensional transverse Ising system, scattering amplitude calculation for tunneling through asymmetric barrier (useful for quantum kinetically constrained system) are given in the appendices.

arXiv:cond-mat/0312611Dec 23, 20032 citations

Quantum Optimization: Spin Glasses and Wavefunction Annealing

Javier Rodríguez-Laguna, Giuseppe E. Santoro

Bulletin of the American Physical SocietyMar 7, 20070 citations

Quantum annealing in a kinetically constrained system

Arnab Das, Bikas K. Chakrabarti, Robin B. Stinchcombe

Classical and quantum annealing is discussed in the case of a generalized kinetically constrained model, where the relaxation dynamics of a system with trivial ground state is retarded by the appearance of energy barriers in the relaxation path, following a local kinetic rule. Effectiveness of thermal and quantum fluctuations in overcoming these kinetic barriers to reach the ground state are studied. It has been shown that for certain barrier characteristics, quantum annealing might by far surpass its thermal counter part in reaching the ground state faster.Classical and quantum annealing is discussed in the case of a generalized kinetically constrained model, where the relaxation dynamics of a system with trivial ground state is retarded by the appearance of energy barriers in the relaxation path, following a local kinetic rule. Effectiveness of thermal and quantum fluctuations in overcoming these kinetic barriers to reach the ground state are studied. It has been shown that for certain barrier characteristics, quantum annealing might by far surpass its thermal counter part in reaching the ground state faster.

arXiv:cond-mat/0502167Physical Review EAug 1, 200538 citations

Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems

Benjamin Everest, Matteo Marcuzzi, Juan P. Garrahan +1 more

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

arXiv:1602.05839Physical review. ENov 4, 201620 citations

We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between

d

-dimensional quantum system with a

(d+1)

-dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the

\pm J

model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses. We have also breifly discussed the possibility of Quantum Annealing in context of kinetically constrained systems. Mean-field calculation for BCS superconductivity, Real-space RG calculation for one dimensional transverse Ising system, scattering amplitude calculation for tunneling through asymmetric barrier (useful for quantum kinetically constrained system) are given in the appendices.