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Quantum Ising model is an exactly solvable model of quantum phase transition. This paper gives an exact solution when the system is driven through the critical point at finite rate. The evolution goes through a series of Landau-Zener level…
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or…
We study non-equilibrium dynamics for an ensemble of tilted one-dimensional atomic Bose-Hubbard chains after a sudden quench to the vicinity of the transition point of the Ising paramagnetic to anti-ferromagnetic quantum phase transition.…
We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising…
CoNb$_2$O$_6$ is a unique magnetic material. It features bulk three-dimensional magnetic order at low temperatures, but its quantum critical behavior in a magnetic field is well described by the one-dimensional transverse-field Ising…
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal…
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the…
Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce different non-equilibrium regimes…
Traditional simulated annealing utilizes thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. We compare…
We study the effects of symmetry-breaking defects at continuous quantum transitions (CQTs), which may arise from localized external fields coupled to the order-parameter operator. The problem is addressed within renormalization-group (RG)…
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour…
We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q>4, separating the…
With Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the…
We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for…
When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a…
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…
We consider the Blume-Capel model with the quantum tunneling between the excited states. We find a magnetically ordered phase transition induced by quantum fluctuation in a model. The model has no phase transition in the corresponding…
We address the out-of-equilibrium dynamics of a many-body system when one of its Hamiltonian parameters is driven across a first-order quantum transition (FOQT). In particular, we consider systems subject to fixed boundary conditions,…
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum…
We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is…