Related papers: Dynamical quantum phase transitions: a review
Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to…
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
Dynamical quantum phase transitions (DQPTs) are non-equilibrium transitions characterized by the orthogonality between an initial quantum state and its time-evolved counterpart following a sudden quench. Recently, studies of this phenomenon…
Quantum many body system in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, nonequilibrium behaviour of quantum many body systems remains elusive, out of the range of such a well…
A sweep through a quantum phase transition by means of a time-dependent external parameter (e.g., pressure) entails non-equilibrium phenomena associated with a break-down of adiabaticity: At the critical point, the energy gap vanishes and…
The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium…
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only…
Nonequilibrium phase transitions are discussed with emphasis on general features such as the role of detailed balance violation in generating effective (long-range) interactions, the importance of dynamical anisotropies, the connection…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent many-body system, it can occur in an…
Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality to the non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…