Dynamical quantum phase transitions: a review

Abstract

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

Static and dynamic phases of a Tonks–Girardeau gas in an optical lattice

“…The large fluctuations observed in the coherence,which is an order parameter that distuingushes the pinned and superfluid phases,is therefore a manifestation of the underlying incommensurate-commensurate transition. This aligns our results with other indications that critical points and regions introduce large fluctuations in the dynamics of order-parameters [2,8,15,16,[63][64][65].…”

“…Sudden perturbations are a powerful method for studying many-body effects in quantum systems, and for TG gases notable examples that have been investigated in recent years include the orthogonality catastrophe and decay [57][58][59][60][61][62], persistent currents and probing superfluidity [33-38, 41, 42]. Such exploration of the nonequilibrium dynamics can be used to further characterize the different phases we have examined in the static model, and quenches can be used to detect phase transitions due to the creation of non-trivial dynamics induced by large quantum fluctuations at criticality [13][14][15][16][17].…”

“…These defects promote dynamics as they preserve a degree of coherence and allow the system to attain superfluid-like properties. Quantum phase transitions in these systems can be probed by switching the control parameter across a critical point [13][14][15][16][17][18]. Additionally, the transport properties of such systems can be linked to classical models of friction which describe stick-slip motion between two surfaces [19][20][21][22][23], an effect which has been recently observed [24][25][26].…”

Observation of Dynamical Quantum Phase Transitions with Correspondence in an Excited State Phase Diagram

“…Fortunately, the model Hamiltonian Eq . (1) actually describes a system of N spin-1 particles with effectively infinite-range interactions [2]; this enables us to characterize the dynamical phase transition by alternative finite-time observables: ρ 0,peak ≡ ρ 0 (t = τ peak ) and δρ 0,peak = δρ 0 (t = τ peak ), the value of ρ 0 and the standard deviation of ρ 0 at the first peak of the spin oscillations, respectively [see Fig. 2] [2].…”

Learning phase transitions from dynamics

“…This approach does not rely on thermal equilibrium, and applies very naturally to time-dependent systems. It is therefore particularly suited for the identification of dynamical as well as Floquet phases [30][31][32][33][34][35][36][37][38][39].…”